■332.5 

H Has 


FOURTH  ANNUAL  PUBLICATION 


Colorado  College 
Studies. 


PAPERS  R AD  BEFORE  THE  COLORADO  COLLEGE 


SCIENTIFIC  SOCIETY 


COLORADO  SPRINGS, 


COLORADO, 


THE  GAZETTE  PRINTING  COMPANY, 
COLORADO  SPRINGS,  COLO. 


UNIVERSITY  OF  ILLINOIS 
LIBRARY 


Class 

"537..  5 


Book  Volume 


Ja  09-20M 


FOURTH  ANNUAL  PUBLICATION. 


Colorado  College 
Studies. 


PAPERS  READ  BEFORE  THE  COLORADO  COLLEGE 
SCIENTIFIC  SOCIETY. 


COLORADO  SPRINGS,  COLORADO. 

1893. 

cr  ^ a \ — 

Dee.  p . 4- b 
\ 


THE  GAZETTE  PRINTING  COMPANY, 
COLORADO  SPRINGS,  COLO. 


3 3 ^ 


« • • »««•* 

« * * * 9 • • • 4 

% '•  * * * • t*  ! « 

' '■' OfFiCEtfS,  1893 


President,  --------  William  Strieby. 

Vice-Presidents,  ------  ( W.  P.  Mustard. 

( L.  R.  Ehrich. 

Secretary,  -------  Florian  Cajori. 

Treasurer, Frank  H.  Loud. 


PLACE  OF  MEETING, 

Palmer  Hall,  Colorado  College. 


CONTENTS. 


Announcement, 


PAGE. 

- 4 


The  Circular  Locus,  ... 

F.  H.  Loud. 

On  the  Eight  Lines  Usually  Prefixed  to  Horat.  Serin.  1. 10, 
W.  P.  Mustard. 


State  Bank  Notes,  - A~ 

• ' - -4:0 

W.  M.  Hall. 


23152 


ANNOUNCEMENT. 


The  following  is  a complete  list  of  the  papers  read  at 
the  monthly  meetings  of  the  Colorado  College  Scientific 
Society  during  the  past  year.  Three  of  the  papers  are 
printed  in  full  in  this  pamphlet,  while  others  will  be  pub- 
lished elsewhere. 

October  18 , 1892  : 

Folk  Etymology  in  Latin,  W.  P.  Mustard. 

November  18,  1892: 

A Construction  for  the  Imaginary  Points 

and  Branches  of  Plane  Curves,  - - F.  H.  Loud. 

December  16,  1892: 

State  Bank  Notes,  - W.  M.  Hall. 

January  27,  1898: 

Friction  Tests  in  Water-pipes  and  Fire- 
hose, ------  W.  Strieby. 

February  24,  1893: 

Prayer  in  a Universe  of  Law,  - - E.  S.  Parsons. 

March  24,  1893  : 

Acidimetry,  - - - - D.  J.  Carnegie. 

On  the  Eight  Lines  Usually  Prefixed  to 

Horat.  Serin.  I.  10,  - - W.  P.  Mustard. 

April  28,  1893: 

Kant’s  Theory  of  Space  and  Time,  - - Marion  McG.  Noyes. 

On  the  Multiplication  of  Semi-convergent 

Series, - Florian  Cajori. 

May  19, 1893: 

The  Essential  Element  of  Religion,  - - F.  R.  Hastings. 

Multipolar  Dynamos,  - - - - Florian  Cajori. 

The  Circular  Locus,  - - F.  H.  Loud. 


< 


THE  CIRCULAR  LOCUST 

Geometrically  Constructed  to  Show  Imaginary  Values  of  the 
Varices.  . : * * „ , 

*5  ■' ' % 3 D D 5,  ) 5 O 


By  FRANK:  H;.  £jO^ID. 


In  the  paper  on  “A  Geometrical  Construction  for  the 
Imaginary  Points  and  Branches  of  Plane  Curves,”  which 
I read  before  this  society  on  November  18,  1892,  the  gen- 
eral method  of  construction  therein  outlined  was  illus- 
trated by  the  simple  example  of  the  equation  x2+Y2=r2; 
and  it  was  shown  by  a diagram  how  the  full  significance  of 
this  equation,  for  imaginary  as  well  as  real  values  of  the 
variables,  may  be  geometrically  interpreted  by  the  aid  of 
additional  curves,  accompanying  the  circle  described 
around  the  origin.  A more  full  and  methodical  treatment 
of  the  theory  of  this  plan  of  construction,  in  its  general 
application,  has  since  been  contributed  to  the  Annals  of 
Mathematics , but  at  the  date  of  the  present  reading  has 
not  appeared  in  print.  It  is  the  object  of  the  present 
paper  to  continue  somewhat  further  the  treatment  of  the 
circular  locus  just  mentioned,  as  a special  case  of  the  gen- 
eral theory,  borrowing,  from  the  two  papers  above  named, 
as  much  as  may  be  necessary  to  render  this  intelligible  to 
a reader  who  has  seen  neither  of  the  others. 

The  principle  of  construction  employed  is  of  course 
based  upon  the  well-known  geometric  interpretation  of  im- 
aginaries,  in  which  a+ia  is  represented  by  a line  drawn 
from  the  origin  to  a point  a units  to  the  right  of  a vertical 
axis  and  « units  above  a horizontal  axis,  called  the  imagi- 
nary and  the  real  axis  respectively. 

The  apparatus  postulated  in  this  usual  representation 
of  imaginaries — a pair  of  rectangular  axes  in  a plane — 
coincides  precisely  with  that  of  the  still  more  familiar 
Cartesian  method  of  translating  algebraic  equations  into 


6 


Colorado  College  Studies. 


geometric  forms,  upon  which  is  reared  the  edifice  of  ana- 
lytical geometry.  In  the  customary  treatment  of  the  latter, 
while  imaginary  values  of  the  variables  appear  frequently 
in  the  algebraic  work’  and  are  recognized  as  of  high  im- 
portance to  the  theory  of  curves  (witness  the  “circular 
points  at  infinity’'),  they  ace  excluded  from  geometric  in- 
terpretation. This  is  not  necessary.  Imaginaries  may  be 
admitted,  with  Treat”  quantities,  into  the  constructions  as 
well  as  the  arguments  or  analytical  geometry,  if  we  are 
content  to  lay  aside  that  habit  of  associating  each  axis 
with  a single  variable,  which  has  resulted  in  the  names 
“axis  of  X”  and  “axis  of  Y”  respectively.  Let  us  regard 
these  lines  rather  as  an  axis  of  reals  and  an  axis  of  imagi- 
naries, and  then  express  the  usual  Cartesian  method  of 
locating  a point  by  its  coordinates,  by  saying  that  the  point 
(x,  y)  means  the  point  at  the  extremity  of  the  vector  x+zy. 
When  x and  Y are  real,  this  will  locate  the  point  just  as 
Descartes  does,  but  if  either  coordinate  be  imaginary,  the 
point  has  still  a definite  position  in  the  plane.  Thus  if 
x=5— 2i and  y=4  + 3z  we  find  x + 2Y=o— 2i+4i— 3=2+2t, 
and  the  point  is  situated  2 units  to  the  right  of  one  axis, 
and  2 above  the  other,  just  as  if  its  coordinates  were  2,  2. 

Thus,  when  imaginaries  are  admitted,  any  point  of  a 
plane  serves  for  the  geometric  representation  of  an  infinite 
number  of  sets  of  coordinates,  all  distinct  from  one  an- 
other, and  we  can  no  longer  infer  from  the  position  alone 
of  a point  what  are  its  coordinates.  If  we  are  informed 
by  some  other  means  what  is  the  imaginary  part  of  each 
coordinate,  then  this  knowledge,  combined  with  that  of  the 
position  of  the  point,  suffices  to  determine  the  real  part, 
and  hence  the  coordinates  in  full.  Thus  in  the  instance 
given,  if  we  know  that  x + ir=2-f  2i,  and  that  the  imagi- 
nary part  of  x is  —2  i,  we  find  by  subtraction  that  the  im- 
aginary part  of  iy  is  4 i,  hence  that  the  real  part  of  Y is  4. 
In  like  manner  may  be  found  the  real  part  of  x. 

An  equation  between  the  variables,  such  as  x2+y2=?'2, 
serves  to  restrict  the  number  of  sets  of  coordinates  belong- 
ing to  any  one  point;  never  depriving  any  point,  however, 


The  Circular  Locus. 


7 


of  its  capacity  of  representing  at  least  one  such  set.  To 
render  visible  tliis  effect  of  the  equation,  it  is  necessary  to 
indicate,  for  points  in  different  parts  of  the  plane,  by  what 
coordinates  they  may,  consistently  with  the  equation,  be 
represented;  and  this  is  effected,  as  already  mentioned,  by 
indicating  the  imaginary  part  of  each  coordinate.  If  a 
line  is  drawn  through  all  these  points  of  the  plane  for 
which  the  imaginary  part  of  x has  a certain  constant  value, 
say  li,  another  through  all  those  points  for  which  its  value 
is  2 1,  etc.,  then  this  system  of  lines  wull  indicate  to  the  eye 
the  value  of  the  imaginary  part  of  x for  all  points  of 
the  plane.  Another  series  of  lines  will  indicate  in  the 
same  way  the  manner  in  which  the  imaginary  part  of  Y 
varies  over  the  plane;  and  when  these  two  things  are  known 
for  any  point,  the  real  parts  of  the  coordinates  become  also 
known,  and  the  geometric  significance  of  the  equation  is 
fully  set  forth.  It  is  true  that  unless  a point  be  situated 
exactly  on  one  of  the  lines  of  each  series,  its  coordinates 
are  only  approximately  indicated;  but,  as  will  be  seen,  it 
will  always  be  possible  to  draw  a line  of  each  set  through 
any  assigned  point  of  the  plane,  and  ascertain  the  value  of 
the  coefficient  of  i which  remains  constant  upon  that  line; 
thus  the  determination  of  the  coordinates  may  be  made 
precise. 

To  these  lines  I have  ventured  to  give  the  name  of 
comitants,  designating  the  two  series  as  accountants  and 
?/-comitants  respectively,  and  affixing  to  either  name  the 
number  or  symbol  denoting  the  constant  value  of  the  co- 
efficient of  i in  the  expression  for  the  coordinate  of  any 
point  upon  it.  Thus  the  accountant  p is  defined  to  mean 
a line  (or  curve)  drawn  through  every  point  for  which  the 
imaginary  part  of  the  value  of  x has  the  value  ip. 

I will  also  adopt  in  the  remainder  of  this  paper,  the 
rule  of  denoting  by  small  capitals  A,  B,  etc.,  quantities 
which  are  entirely  unrestricted  in  value,  and  hence  are,  in 
general,  complex;  while  for  their  real  parts  I use  italic  let- 
ters, and  Greek  letters  for  the  coefficients  of  the  imaginary 


8 


Colorado  College  Studies. 


unit.  Thus  A =a+ia,  b=&  + ?’/3,  etc.  The  Greek  letter  an- 
swering to  c is  taken  to  be  y,  and  that  answering  to  Y to 
be  rj. 

To  return  to  the  comitants,  it  is  plain  that  one  of  each 
series  is  of  chief  importance,  namely,  the  comitant-zero. 
This  may  be  compared  to  the  equator  on  a map,  while  the 
comitant  +1  and  the  comitant  — 1 are  on  opposite  sides  like 
parallels  of  latitude.  The  ^-comitant  0 passes  through  all 
the  points  for  which  x is  real,  and  the  ^/-comitant  0 through 
all  those  for  which  Y is  real,  so  that  all  “real  points”  of 
the  locus — that  is,  those  having  both  coordinates  real — 
must  lie  on  both  these  lines.  For  all  real  curves,  there- 
fore, the  comitants  zero  will  have  a common  arc,  and  this 
arc  will  be — or,  at  least,  will  include — the  curve  itself,  as 
known  to  the  ordinary  constructions  of  analytical  geom- 
etry. Thus  for  the  equation  of  our  present  example, 
x2  + Y2=r2,  the  ^-comitant  0 consists  of  the  circle  of  radius  r 
described  about  the  origin,  and  in  addition  of  a line  coin- 
ciding with  the  real  axis.  The  ^/-comitant  0 consists  of 
the  same  circle  with  the  addition  of  the  axis  of  imagina- 
ries.*  The  other  comitants,  of  either  series,  are  cubic 
curves  situated  on  opposite  sides  of  the  axis  named,  and 
having  oval  branches  within  the  circle,  as  will  shortly  be 
seen. 

A rule  for  constructing  the  comitants  by  points  may  be 
derived  by  inspection  of  the  equation.  For  the  £c-comi- 
tants,  we  may  put  the  latter  in  the  form  — y2=x2— r2,  when 
we  have,  by  extraction  of  the  square  root,  and  the  addition 
of  x to  each  member, 

x-H'y=x±\/ (x  + r)  (x — r). 

The  mean  proportional  between  x + r and  x— r,  which, 
as  the  radical  indicates,  is  to  be  found,  is  to  be  understood 
of  course  not  merely  as  having  the  length  implied,  in  the 
Euclidean  use  of  the  word,  but  as  bisecting  the  angle  at 

* Beside  having  the  circle  in  common,  these  two  comitants  zero  intersect 
also  at  the  origin,  for  this  point  of  the  locus  may  be  regarded  as  having  either  of 
its  co-ordinates  real,  but  since  the  latter  cannot  both  be  real  at  once,  the  origin 
is  not  included  in  the  real  part  of  the  locus. 


The  Circular  Locus. 


9 


the  origin  formed  by  the  two  vectors  x + r and  x— r.  Simi- 
larly, the  principle  of  vector-addition  is  to  be  borne  in 
mind  in  uniting  the  result  with  the  term  x.  The  ordinary 
geometric  constructions  of  a bisectrix  and  a mean  propor- 
tional may  be  combined  with  a fair  degree  of  convenience 
as  follows:  Let  the  two  axes,  OJ  and  01, 


and  the  circle  of  radius  r about  the  origin  be  first  drawn,  in 
ink,  or  so  as  to  remain  permanently  through  the  construc- 
tion. If  the  ££-comitant  p is  to  be  drawn,  where  p is  a given 
quantity,  let  a point  M be  taken  on  the  axis  of  imaginaries, 
at  a distance  p above  the  origin;  also  a point  S midway 
between  O and  M;  and  let  lines  MN  and  ST  be  drawn  par  - 
allel to  the  real  axis  to  an  indefinite  length.  These  two 
lines  will  remain  during  the  construction  of  a single  comi- 
tant,  but  all  that  follow  must  be  erased  and  drawn  anew 
for  each  point  constructed.  On  MN  take  any  point  X, 
and  on  the  same  line  two  points,  H and  K,  at  distances 
equal  to  r,  on  opposite  sides  of  X.  Of  these,  let  H be  on 
the  side  of  X opposite  M.  Draw  OH.  With  center  O and 
radius  OK  describe  an  arc  intersecting  OH  at  G,  and  at  G 
erect  a perpendicular  to  OH.  From  center  U (the  point 
where  OH  meets  ST)  with  radius  UH,  describe  an  arc  cut- 
ting this  perpendicular  at  Q.  From  K and  G,  with  equal 


10 


Colorado  College  Studies. 


radii  of  any  convenient  length,  describe  arcs  meeting  at  F; 
draw  OF,  and  on  it  take  OL  and  OL'  in  opposite  direc- 
tions, each  equal  to  OQ.*  On  the  side  of  LOL'  toward  X, 
describe  arcs  from  centers  L and  L',  with  radius  OX;  and 
intersect  each  of  them  by  an  arc  drawn  from  center  X with 
radius  OL.  Then  P and  P',  the  points  of  intersection,  will 
be  points  on  the  comitant  curve,  one  on  the  infinite  branch, 
the  other  on  the  oval.  Two  more  points  on  the  same  comi- 
tant are  situated  symmetrically  to  these,  on  the  opposite 
side  of  the  imaginary  axis.  Also,  the  aucomitant  —;j.  is 
equal  to  the  ic-comitant  /*,  and  the  real  axis  is  an  axis  of 
symmetry  to  the  two  curves.  Further,  if  either  of  them 
be  rotated  through  a right  angle,  a ?/-comitant  is  produced; 
but  it  must  be  noted  that  while,  for  all  positive  values  of 
fi,  the  infinite  branch  of  the  a?-comitant  ;j.  is  situated  above 
the  real  axis,  that  of  the  ^/-comitant  / x is  to  the  left  of  the 
axis  of  imaginaries.  Thus  a single  construction  virtually 
determines  sixteen  points — four  on  each  of  two  a?-comi- 
tants  and  as  many  more  on  two  ?/-comitants. 

Each  comitant,  excepting  the  comitants  zero,  proves 
when  drawm  to  consist  of  a conchoidal  and  an  oval  branch, 
the  former  approaching  at  infinity  a line  drawn  parallel  to 
an  axis  (the  real  axis  in  the  case  of  aucomitants)  and  at  a 
distance  therefrom  equal  to  double  the  coefficient  (//.)  of 
which  distinguishes  the  particular  comitant;  while  the  oval 
lies  on  the  opposite  side  of  this  axis,  touching  the  latter  at 
the  origin.  The  breadth  of  each  branch,  in  a direction 
perpendicular  to  the  above-named  axis,  is  the  same,  and 
is  easily  found  to  be  u2+/P— ,u;  while  r2+/ ^2+/jt  is  the 

greatest  ordinate  of  the  curve,  belonging  to  the  point  where 
the  conchoidal  branch  cuts  the  other  axis,  which  divides 
it  symmetrically.  Regarding  together  all  the  comitants  of 
one  series,  it  is  apparent  that  all  have  a common  point  at 

* Another  method  of  finding  a geometric  mean  between  two  lines  which  ex- 
tend from  a common  point  is  as  follows  : First,  bisect  the  angle  of  the  lines  and 
also  its  adjacent  supplementary  angle.  On  the  latter  bisectrix  lay  off  half  the 
longer  line,  and  from  its  extremity,  in  both  directions,  half  the  shorter,  thus 
obtaining  the  half  sum  and  half  difference  of  the  lines.  From  the  extremity  of 
the  half-difference,  with  radius  equal  to  the  half  sum,  cut  off  on  the  bisectrix  of 
the  angle  a segment,  which  will  be  the  required  mean  proportional. 


The  Circular  Locus. 


11 


infinity,  also  all  the  ovals  are  mutually  tangent  at  the 
origin.  Beginning  with  a very  small  value  of  /*,  the  corre- 
sponding comitant  of  course  lies  near  the  comitant  zero, 
which  consists  of  a circle  and  a line;  and  it  is  seen  that 
the  conchoidal  part  of  the  comitant  answers  to  one  semi- 
circumference  and  to  that  part  of  the  line  which  is  outside 
the  circle,  and  lies  just  outside  these  parts  of  the  comitant 
zero.  The  oval,  on  the  other  hand,  answers  to  the  other 
half  the  circumference  and  to  its  diameter,  and  lies  inside 
the  semicircle  close  against  the  boundary.  Accordingly, 
its  curvature  is  rapid  on  the  side  remote  from  the  origin, 
while  near  the  latter  it  is  almost  straight.  The  succeeding 
comitants  have  their  conchoidal  parts  successively  further 
and  further  from  the  axis,  each  encompassing  its  predeces- 
sor, and  more  nearly  straight  than  it,  while  the  ovals  lie 
each  one  within  the  preceding,  and  are  rounder  as  well  as 
smaller.  Hence  for  \j.—  qc,  the  comitant  should  consist  of 
a point  (the  origin),  and  a line  at  an  infinite  distance. 

We  are  thus  able  to  construct  and  describe  the  systems 
of  comitants  from  the  equation  x2-f  Y2=r2  alone;  but  if 
we  wish  to  determine  the  order  of  these  curves,  so  as  to 
study  them  in  the  light  of  related  forms,  it  becomes  de- 
sirable to  pass  to  new  equations.  In  the  article  already 
mentioned,  contributed  to  the  Annals  of  Mathematics,  it  is 
shown  that  from  the  equation  of  any  locus  we  may  derive 
that  of  another,  whose  real  part  shall  coincide  with  any 
specified  comitant  curve  of  the  given  locus.  In  the  present 
instance  we  shall  obtain,  for  the  general  ^-comitant — the 
ic-comitant  £ — the  following  result: 

x2y+y3—r2y—2c  (x2-\-y2)  = 0; 
and  for  the  ?/-comitant  rh 

x*+xy2—r2x+ 2rj  (x2+y2)  = 0. 

These  may  be  called  the  “equations  of  the  comitants,”  for 
the  sake  of  brevity  of  expression,  if  it  be  borne  in  mind 
that  from  our  present  point  of  view  the  only  equation 
which  truly  represents  the  comitants  and  nothing  more , is 


12 


Colorado  College  Studies. 


that  which  at  the  same  time  represents  them  all,  viz.,  the 
equation  x2+Y2=r2. 

The  new  equations  show  that  all  the  comitants  are 
cubics;  and  the  existence,  as  previously  ascertained,  of  an 
oval  branch  in  each,  at  once  refers  them  to  that  one  of  the 
genera  of  Cayley  and  Salmon  which  consists  of  the  projec- 
tions of  the  “ parabola  cum  ovali If  a more  minute 
identification  is  desired,  a transformation  of  coordinates, 
easily  effected,  throws  either  equation  into  the  standard 
form  discussed  by  Sir  Isaac  Newton  in  his  “ Enumeratio 
Lineavum  Tertii  Ordinis .”  The  curves  thus  prove  to  be  of 
the  kind  described  by  him  as  “ defective  hyperbolas  having 
a diameter,”  and  to  belong  to  the  species  numbered  40, 
whose  distinguishing  mark  is  the  presence  of  the  oval  on 
the  concave  side  of  the  conchoidal  branch.  To  write  either 
equation  in  the  form  adopted  by  Plucker  as  a standard, 
no  change  of  axes  is  necessary,  but  the  equation  of  the 
accountants,  for  instance,  becomes  by  a purely  algebraic 
modification, 

(2/-2e)[^+^-0]-^2r#+02/+|r^=O. 


In  this  expression,  the  existence  of  the  asymptote 


(0-2 


0)  and  of  the  “ asymptotic  point  ” 


becomes 


manifest,  as  also  the  position  of  the  “satellite  line”  whose 

/ ?"2  \ 1 

equation  is  ^2r£-f  — j?/=— r2£:  Among  the  diametral  de- 

fective hyperbolas — or,  to  use  language  better  correspond- 
ing to  the  vocabulary  of  Plucker,  among  cubics  whose  single 
asymptote  is  osculating  — the  group  numbered  xxxiv  is 
distinguished  by  the  fact  that  that  line  passes  through  the 
asymptotic  point,  while  the  next  preceding  group,  xxxiii, 
differs  from  all  others  in  which  the  asymptote  and  asymp- 
totic point  are  separate,  by  the  fact  that  the  satellite  line 
does  not  cut  the  curve.  In  the  special  case  in  which  £ has 


the  value  — , the  comitant  belongs  to  xxxiv,  otherwise  to 
4 

xxxiii.  In  either  case,  the  existence  and  position  of  the 


The  Circular  Locus. 


13 


oval  determine  the  species,  in  the  classification  of  PI  ticker 

V 

as  in  that  of  Newton;  so  that  if  c=— , the  curve  is  of 

4 

species  152,  but,  for  other  values  of  of  species  148. 

The  equations  of  the  comitants  also  suggest  a process 
of  geometrical  construction  entirely  different  from  that 
deduced  from  the  original  equation  of  the  locus.  (See  Fig. 


II. ) If,  as  before,  it  is  desired  to  construct  the  a?-comitant  fi, 
let  the  axes  and  the  circle  of  radius  r and  center  O be  again 
drawn,  and,  in  addition,  a semicircle  having  for  its  diameter 
that  radius,  OC,  of  the  former  circle  which  extends  along  the 
imaginary  axis  in  the  direction  indicated  by  the  sign  of  //. 
Draw  also,  through  B,  one  of  the  points  in  which  the  circle 
of  radius  r meets  the  real  axis,  a tangent  to  this  circle. 
All  the  foregoing  may  remain  unerased  during  the  entire 
construction.  On  the  tangent  last  drawn,  take  points  G 
and  H,  so  that  BG=/j-  and  BH=2/^..  Draw  OG,  and  pro- 
duce it  sufficiently,  so  that  a distance  equal  to  GB  may  be 
laid  off  from  G on  the  produced  part,  to  E,  while  the  same 
distance  from  G toward  O,  fixes  the  point  D.  Then  OE 
will  be  the  maximum  distance  of  the  conchoidal  branch 
and  OD  that  of  the  oval  branch,  from  the  axis  of  reals,  and 
the  extremities  of  these  maximum  ordinates  are  to  be 
located  on  the  other  axis,  in  opposite  directions  from  the 


14 


Colorado  College  Studies. 


origin.  In  finding  other  points,  the  construction  must 
proceed  somewhat  differently  for  the  two  branches.  For 
the  infinite  branch,  take  on  the  line  BG  a distance  BK 
greater  than  BH  and  less  than  OE.  Draw  BC  and  OK, 
and'  call  their  point  of  intersection  F.  Draw  HF,  inter- 
secting the  imaginary  axis  at  L,  and  then  draw  LM  paral- 
lel to  the  real  axis  and  meeting  the  semi-circumference, 

^of  radius  ^ at  M.  Draw  OM,  and  produce  it  to  meet 

the  circle  of  radius  r at  N.  Draw  NQ,  parallel  to  MC, 
meeting  the  imaginary  axis  at  Q.  Finally,  describe  about 
O,  with  radius  OQ,  an  arc  meeting  at  P and  P'  a parallel 
to  the  real  axis  drawn  through  Iv.  Then  P and  P'  are 
points  of  the  conchoidal  branch. 

For  the  oval,  extend  the  tangent  GB  on  the  opposite 
side  of  the  axis  of  reals,  and  take  BK'  in  that  direction,  of 
any  length  not  exceeding  OD.  Draw  OK'  and  CH,  to  in- 
tersect at  F ' , and  then  F ' B,  meeting  the  imaginary  axis 
at  S.  Through  S,  a parallel  to  the  real  axis  is  to  be  drawn, 
meeting  the  semi-circumference  at  T.  Then  an  arc,  with 
radius  OT,  described  about  O,  will  meet  the  parallel  to  the 
real  axis  drawn  through  K',in  points  belonging  to  the 
oval. 

If  a parallel  ruler  is  used  in  drawing,  this  construction 
may  prove  more  convenient  than  the  preceding,  since  the 
compasses  will  have  to  be  adjusted  only  once  in  locating 
each  pair  of  new  points.  It  should  be  mentioned  that  after 
the  distances  OD  and  OE  have  been  determined,  we  may, 
if  convenience  require,  replace  the  points  B,  G,  H,  K,  K', 
on  a tangent  to  the  circle,  by  points  at  equal  heights  on 
any  other  parallel  to  the  imaginary  axis. 

In  each  of  the  foregoing  constructions  for  a comitant  fi 
it  has  been  assumed  that  the  value  of  t*.  is  directly  given. 
An  important  modification  of  the  problem  may  be  stated 
as  follows:  Through  any  given  point  of  the  plane  to 
draw  the  comitants  of  a circular  locus  of  given  radius, 
whose  center  is  at  the  origin.  Here  it  is  necessary  to  de- 
termine at  the  outset  the  quantity  (coefficient  of  i)  which 


The  Circular  Locus. 


15 


characterizes  each  of  the  required  comitants,  and  for  this 
purpose  the  comitant  equations  may  be  employed.  Thus, 
in  the  case  of  an  a?-comitant,  the  equation  may  be  written 
y (x2  4- y2  — v*  j 

2£=— — ’ a ^ormu^a  which  directly  suggests  the 

following  geometric  process:  Draw  by  the  usual  methods 
the  polar  of  the  given  point  with  respect  to  the  circle  of 
radius  r,  and  from  the  point  in  which  this  polar  meets  the 
line  joining  the  given  point  to  the  origin  draw  a parallel 
to  the  real  axis,  then  the  perpendicular  distance  from  this 
line  to  the  given  point  is  equal  in  absolute  magnitude  to 
double  the  quantity  £,  answering  to  the  u of  the  preceding 
constructions.  Having  found  this  quantity,  the  comitant 
is  constructed  as  before. 

It  is  to  be  observed  that  when  £ and  t\  are  found  by  this 
process,  the  coordinates  of  the  given  point  are  fully  known, 
hence  this  construction  solves  also  the  problem:  To  deter- 
mine geometrically  the  coordinates  of  a given  point  of  a 
plane,  when  regarded  as  a point  of  a circular  locus  of  given 
radius,  having  the  origin  as  center. 

Having  now  sufficiently  considered  the  form  and  posi- 
tion of  the  comitant  curves  which  make  up  the  circular 
locus,  the  next  step  will  be  to  examine  the  most  important 
properties  of  the  locus  as  they  are  discussed  in  the  elemen- 
tary analytical  geometry,  and  observe  what  new  light  is 
shed  by  the  present  construction  upon  the  familiar  pro- 
cesses and  results. 


“A  right  line,”  it  is  commonly  said,  intersects  the  circle 
in  two  points,  which  may  be  real  and  discrete,  coincident, 
or  imaginary.  Just  as  the  “circle,”  here  used  to  mean  the 
geometric  equivalent  of  the  equation,  is  in  the  present  in- 
terpretation replaced  by  a double  system  of  curves,  together 
forming  the  circular  locus , so  the  right  line  gives  place  to 
a double  system  of  lines.  These  intersect  the  comitants 
of  the  circular  locus  in  every  part  of  the  plane,  but  since 
these  indefinitely  numerous  intersections  of  the  separate 
comitants  are  not  liable  to  be  confused  with  the  two  special 
points  mentioned  in  the  theorem,  the  word  “intersect” 


16 


Colorado  College  Studies. 


may  be  retained,  and  the  proposition  will  read,  “A  circular 
and  a linear  locus  intersect  at  two  points.”  By  a point  of 
intersection  of  two  loci  must  of  course  be  meant  one  whose 
coordinates,  when  it  is  regarded  as  a point  of  the  one  locus, 
are  the  same  as  when  it  is  taken  to  belong  to  the  other. 
If  such  a point,  then,  lies  on  the  ^-comitant  £ of  one  locus, 
it  is  on  the  a?-comitant  £ of  the  other  (the  £ having  the 
same  value  for  the  two),  and  a similar  statement  is  true  of 
the  other  system  of  comitants.  Thus  a point  of  intersec- 
tion of  two  loci  may  be  defined  as  a point  in  which  tioo 
comitants  (viz.,  one  of  each  series ) belonging  to  one  locus 
are  met  by  the  corresponding  comitants  of  the  other  locus. 

The  theorem  of  analytical  geometry,  above  quoted,  speci- 
fies not  only  the  number  of  intersections  of  the  two  loci, 
but  their  kinds.  This,  however,  is  done  under  the  tacit 
assumption  that  both  loci  are  real.  The  full  statement 
intended,  therefore,  is  as  follows:  “A  circular  and  a linear 
locus,  each  of  which  has  a real  branch,  intersect  at  two 
points,  which  may  be  real  and  discrete,  real  and  coincident, 
or  conjugate  imaginary.”  The  locus  of  a linear  equation 
with  real  coefficients  (called,  for  brevity,  a real  linear  locus) 
has  the  two  comitants  zero  coinciding  in  a single  right 
line,  while  each  of  the  series  of  comitants  consists  of 
lines  parallel  to  this.  Beal  intersections,  whether  in  dis- 
crete or  consecutive  points,  are  formed  by  the  real  parts 
of  the  two  loci,  just  as  in  the  ordinary  constructions  of 
analytical  geometry.  The  situation  of  the  imaginary  inter- 
sections may  be  easily  studied  by  combining  the  two  equa- 
tions x2  + Y2=r2  and  x cos  <p- f y sin  <f=p , while  assuming 
p>r.  Elimination  gives  x—p  cos  <p±i  sin  y'Sp2 — r2,  and 
Y =p  sin  <p^pi  cos  <p*Sp 2 — r2,  whence 

x + iY  = (p±v/p2— r2)  (cos  sin  <p). 

It  is  at  once  apparent  that  the  two  intersections  lie 
on  the  perpendicular  drawn  from  the  origin  to  the  real 
part  of  the  linear  locus,  at  equal  distances  on  opposite 
sides  of  the  latter,  but  always  on  the  same  side  of 
the  origin.  The  intersection  nearest  the  origin  is  within 
the  real  part  of  the  circular  locus,  since  p — p2 — r2<r, 


The  Circular  Locus. 


17 


hence  the  branches  of  its  comitants  which  are  here  met  by 
the  corresponding  linear  comitants  are  both  ovals,  while  at 
the  other  intersection  of  the  loci,  the  conchoidal  branches 
alone  are  present.  If  p is  made  indefinitely  great,  the 
latter  intersection  recedes  to  infinity,  while  the  former 
approaches  the  origin  as  its  limiting  position.  In  this 
way  is  indicated  the  geometric  representation  of  the  “cir- 
cular points  at  infinity,”  only  one  of  which,  it  appears,  is 
situated  at  an  infinite  distance  on  the  plane,  and  this  one 
must  be  regarded  as  in  an  indeterminate  direction  from 
the  finite  points  of  the  locus.  But  the  further  examination 
of  these  important  points  may  be  deferred  a little  until  the 
subject  of  the  asymptotes  is  reached. 

The  geometric  construction  of  the  finite  imaginary 
points  in  which  the  circular  locus  may  be  intersected 
by  a real  linear  locus  needs  little  further  statement.  The 
real  parts  of  the  loci — the  circle  and  non-secant  line — are 
supposed  given.  A perpendicular  is  to  be  drawn  to  the 
line  from  the  center  of  the  circle  (the  origin),  and  from  its 
foot  a tangent  to  the  circumference.  The  length  of  this 
tangent,  laid  off  on  the  above-mentioned  perpendicular  in 
both  directions  from  its  intersection  with  the  given  line, 
marks  out  the  points  required. 

By  the  aid  of  the  circle  may  also  be  solved  a problem, 
which  may  often  be  required,  viz:  To  draw  other  comitants 
of  a real  linear  locus,  when  the  comitants  zero  (i.  e.,  the 
real  line)  are  given.  The  distance  between  two  comitants 
of  one  system,  say  the  £C-comitant  p and  the  a?-comitant  v, 
for  a given  difference  between  p and  v,  depends  on  the 
direction  of  the  real  line,  and  is  independent  of  the  latter’s 
distance  from  the  origin.  Hence  if  the  given  line  happens 
to  be  a secant,  a parallel  may  be  drawn  to  it  which  will  lie 
outside  the  circumference,  and  then  the  points  of  intersec- 
tion of  the  loci  found  as  above.  Selecting  one  of  these 
points— for  instance,  the  exterior  one — its  distance  from 
the  given  line  proves  to  be  to  the  coefficients  of  i in  its  co- 
ordinates x and  Y,  as  unity  to  sin  <p  and  —cos  <p  respectively. 
The  corresponding  distance  of  the  two  comitants  p will  be 
to  p in  the  same  ratio,  hence  these  distances  are  p cosec  <p 
and  —p  sec  <p. 


18 


Colorado  College  Studies. 


The  rule  that  imaginary  intersections  of  a circular  and 
a linear  locus  must  be  conjugate,  and  hence  discrete,  ceases 
of  course  to  apply  if  the  linear  locus  is  imaginary,  when 
two  imaginary  intersections  may  be  coincident.  In  this 
case,  at  the  point  of  contact  of  the  two  loci  an  £c-comitant 
of  one  must  be  touched  by  the  corresponding  cc-comitant 
of  the  other,  and  also  a ?/-comitant  of  the  first  by  its  cor- 
responding ?/-comitant  of  the  second,  the  two  curves  hav- 
ing in  general  different  directions  at  the  point,  since  in  an 
imaginary  linear  locus  the  two  series,  of  comitants  need 
not  be  parallel  to  each  other.  Two  such  linear  loci,  having 
a real  point  Q in  common,  may  touch  the  circular  locus. 
The  usual  form  of  this  statement,  that  “two  imaginary 
tangents  to  a circle  may  be  drawn  through  any  point  within 
the  latter,”  must  not  be  allowed  to  give  the  impression 
that  the  comitants  of  the  linear  loci,  which  are  the  actual 
tangents,  will  pass  through  the  point  Q.  This  would  of 
course  be  impossible,  since  Q,  as  the  sole  real  point  of  each 
linear  locus,  is  at  the  intersection  of  its  comitants  zero. 
In  fact,  since  the  polar  of  Q with  its  comitants  constitutes 
a real  linear  locus,  intersecting  the  circular  locus  in  the 
points  of  contact,  the  latter  points  must,  as  already  shown, 
be  on  the  perpendicular  from  the  origin  on  this  polar;  that 
is,  on  the  line  OQ. 

The  complete  geometric  construction,  exhibiting  the 
“ tangents  to  a circle  from  a point  within,”  may  be  made 
as  follows:  (See  figure,  page  19). 

The  circle  drawn  around  the  origin  as  center,  and  the 
point  Q (which,  to  avoid  undue  "simplification,  may  be 
assumed  to  be  on  neither  axis)  are  the  only  data  needed. 
The  polar  of  Q is  first  to  be  drawn,  and  the  intersections 
made  by  the  locus  to  which  it  belongs  are  to  be  found  in 
the  manner  just  stated.  These  are  the  points  of  contact. 
By  a previous  construction  the  coordinates  of  T,  one  of 
these  points,  may  be  determined  geometrically,  and  it 
will  be  well  (in  order  to  render  apparent  the  significance 
of  the  subsequent  construction)  to  sketch  at  the  same 
time  the  circular  comitants  which  pass  through  T.  Now 
if  the  algebraic  expressions  for  the  coordinates  of  T be 


The  Circular  Locus. 


19 


Fig.  III. 


M and  N,  the  equation  of  the  tangent  is  MX+NY=r2;  whence 

it  is  seen  that,  for  the  point  of  the  tangent  at  which  x=0, 
u2 

y will  be  - . Accordingly,  that  point  may  be  located  by 


finding  (in  direction  as  well  as  in  magnitude)  a third  pro- 
portional to  the  quantities  N and  r.  For  this  purpose,  if 
the  vector  ON  expresses  the  quantity  n,  while  OR  is  that 
radius  of  the  circle  which  coincides  with  the  real  axis,  an 
angle  ROH  must  be  made  equal  to  NOR,  and  an  angle 
ORH  equal  to  ONR,  when  the  distance  OH,  cut  off  by  the 
bounding  line  of  one  of  these  angles  on  that  of  the  other, 
will  represent  the  value  of  y.  If  OK  make  a positive  angle 
of  90°  with  OH,  and  be  made  equal  to  OH  in  length,  it 
will  represent  iy  and  hence  x + ^y;  so  that  K is  the  point 
of  the  tangent  locus  for  which  x=0.  Rut  this  point  must 
be  on  the  ^-comitant  zero,  and  that  line  is  accordingly  QK. 
A parallel  to  QK  through  T is  the  linear  £c-comitant  at 
that  point,  and  will  be  found  to  touch  the  ^-comitant  of 
the  circular  locus.  Similarly,  by  first  finding  the  point  of 
the  tangent  locus  for  which  Y=0,  the  tangent  ^-comitant 
may  be  constructed;  and  in  like  manner  both  the  comi- 


20 


Colorado  College  Studies. 


tants  of  the  other  tangent  locus  may  be  drawn  through  T', 
the  second  point  of  contact. 

By  a slight  modification  of  this  construction,  a tangent 
may  be  drawn  at  a given  imaginary  point  of  the  locus. 
For  if  T be  given,  the  points  of  the  tangent  locus  for  which 
x and  Y respectively  vanish  may  be  found  as  before,  but  Q 
must  be  determined  in  order  to  obtain  the  directions  of 
the  comitants  zero.  From  the  relations  already  stated  it 
is  easily  shown  algebraically  that  if  OT  be  a given  dis- 
tance d,  then  OQ  is  found  from  the  proportion 
d2  + r2 : r2=2d  : OQ; 

which  admits  of  ready  geometric  construction.* 

Again,  the  construction  of  the  polar  of  an  imaginary 
point  whose  coordinates  are  given  is  obtained  in  a similar 
manner.  For  the  equation  of  the  polar  of  a point  M,  N is 
in  the  same  form  MX-f  NY=?’2  already  used  for  the  tangent, 
hence,  the  points  of  the  required  locus  for  which  x and  Y 
are  severally  zero  are  found  as  before,  but  the  real  point 
must  be  separately  determined.  For  this  purpose  we  may 
put  for  m and  n respectively  their  expanded  values 
n+iv  (where  m,  n,  v and  v are  given  real  quantities),  and 
then  if  we  assume  that  x and  y are  the  real  quantities  x 
and  y , we  can  separate  the  equation  (m-H’/Q  {n-\-v>)y— 

r2= 0 into  two  (since  the  sums  of  the  real  and  imaginary 
terms  must  separately  vanish),  which  will  be  mx-\-ny—  r2=0 
and  [j.x-\-vy= 0.  The  real  point  of  the  locus  is  then  at  the 
intersection  of  two  lines,  whereof  the  former  is  the  polar 
of  a known  point  m,  n;  and  the  latter  is  a line  through  the 
origin,  the  tangent  of  whose  inclination  to  the  real  axis  is 

— — . With  the  determination  of  this  point,  two  points  of 

each  of  the  comitants  zero  become  known,  and  hence  these 
lines  may  be  drawn.  To  fully  construct  the  locus,  how- 
ever, it  is  needful  to  have  the  coordinates  of  one  imaginary 
point,  that  the  distance  between  successive  comitants 


*In  this  is  included  the  solution  of  a problem  relating  to  a comitant  curve 
considered  as  a variety  of  the  cubic,  and  independently  of  its  connection  with 
the  other  comitants  forming  the  locus  ; viz : To  draw  a tangent  at  a given  point 
of  the  curve. 


The  Circular  Locus. 


21 


of  each  series  may  be  known.  Following  the  analogy 
of  the  previous  part  of  the  problem,  we  may  inquire 
for  the  point,  both  of  whose  coordinates  are  pure  im- 
aginaries.  Writing  for  x and  ir\  for  Y,  the  equation 
becomes  (m+^)  — r2=0  and  is  resolved  into 

— fig—vt <j  — r2=0  and  ml -f nt) == 0.  Now  the  point  whose 
coordinates  are  is  and  iy  is  the  same  as  that  whose 
real  coordinates  are  x=  —rh  ?/=!;  hence  the  foregoing 
resolved  equation  may  be  interpreted  as  directing  to 
a point  at  the  intersection  of  two  lines,  one  of  which 
is  the  polar  of  the  known  point  v,  — and  the  other  is 
drawn  through  the  origin  at  an  inclination  to  the  real  axis 

IX 

whose  tangent  is  — . The  perpendicular  distance  of  the 

point  thus  found  from  the  real  axis  is  in  the  same  ratio  to 
its  distance  from  the  sc-comitant  0 as  the  unit  of  linear 
measure  is  to  the  distance  between  the  a?-comitants  0 and  1 ; 
and  a similar  proportion  gives  the  interval  between  suc- 
cessive ?/-comitants. 

Since  every  linear  equation  (unless  its  absolute  term  is 
zero)  may  be  thrown  into  the  form  MX-f-NY=r2,  by  multi- 
plying it  through  by  the  (real  or  imaginary)  ratio  of  r2  to 
this  absolute  term,  we  have  in  the  foregoing  a direction 
for  constructing  all  the  comitants  of  any  such  linear  locus 
given  by  its  equation.  The  coefficients  m and  N,  found  in 
this  way,  are  the  coordinates  of  the  pole  of  the  given  locus. 

The  problem  of  finding  the  points  of  contact  of  the  two 
linear  tangent  loci  which  have  a given  imaginary  point  in 
common  is  equivalent  to  that  of  finding  the  points  of  in- 
tersection of  the  circular  locus  by  the  polar  of  the  given 
point;  and  this  may  be  done  as  follows,  without  the  labor 
of  constructing  the  polar  locus.  The  method  is  based  on 
an  inspection  of  the  result  of  a solution  of  the  two  equa- 
tions x2+Y2=r2  and  MX+NY=r2.  It  is  found  algebraically 

that  x-H‘y= — ?-T-(?,zb\/ r2— m2— N2).  To  express  this  re- 

sult  geometrically,  we  have  first  to  find  >/ m2  + n2,  a mean 
proportional  between  m-M'n  and  m— in;  then  >/ r2—  M2— N2, 


22 


Colorado  College  Studies. 


a mean  proportional  between  r-f ^ m2  + n2  and  r—^ M2-f-N2, 
and  finally  a fourth  proportional  to  M — in,  r,  and 
r±\/  r2— M2— N2. 

If  P is  the  given  point,  whose  coordinates  are  M,  N,  and 
if  M is  the  point  M,  0,  then  MP  is  equal  to  in,  and  by  pro- 
ducing PM  to  Q,  making  MQ=PM,  the  point  m,  — n,  is 
found.  Hence  the  first  step  is  accomplished  when  a dis- 
tance equal  in  magnitude  to  a mean  proportional  between 
OP  and  OQ  is  laid  off  both  ways  from  O on  the  line  bisect- 
ing the  angle  POQ.  From  each  of  the  points  thus  fixed  a 
distance  r is  then  to  be  measured  to  the  right,  parallel  to 
the  real  axis,  so  fixing  the  points  H,  K.  Now  the  angle 
HOK  is  to  be  treated  as  was  POQ;  i.  e.,  on  its  bisector  is 
to  be  laid  off  in  each  direction  from  O a length  equal  to  a 
mean  proportional  between  its  sides,  and  from  each  of  the 
points  so  found  a distance  r measured  to  the  right,  to  the 
points  E and  F respectively.  If  B be  the  right-hand  ex- 
tremity of  that  diameter  of  the  circle  which  lies  on  the 
real  axis,  we  have  next  to  make  a triangle  OET  similar  to 
OQE,  on  the  base  OE  homologous  to  OQ  (and  with  the 
angle  TOE  equal  in  sense  as  well  as  in  magnitude  to  EOQ), 
and  T will  be  one  of  the  required  points  of  contact;  the 
other  having  the  same  relation  to  OF  that  T has  to  OE. 
(Figure  omitted.) 

The  remark  has  been  already  made  that  any  linear 
locus  which  does  not  contain  the  point  0,  0,  may  be  re- 
garded as  represented  by  the  equation  MX-f-NY=r2;  hence 
the  foregoing  construction  of  the  intersections  of  such  loci 
needs  only  to  be  supplemented  by  discussing  those  of  the 
locus  CY=sx,  to  complete  the  treatment  of  linear  intersec- 
tions. Let  the  points  C and  S be  the  extremities  of  vectors 
extending  from  O and  having  the  values  c and  s respec- 
tively, and  let  P be  the  point  whose  (imaginary)  coordi- 
nates are  c,  s.  Produce  PC  to  Q making  CQ=PC,  then  the 
vectors  OP,  OQ  are  c-H’s  and  c—is  respectively;  so  that 
OL  and  OL'  (denoted  by  ±l)  will  represent  =t\/c2-|-s2, 
if  L and  L ' be  taken  on  the  bisector  of  the  angle  POQ  and 
at  distances  each  way  from  O equal  to  the  mean  propor- 
tional. between  the  lengths  OP,  OQ.  The  coordinate  x of 


The  Circular  Locus. 


23 


the  point  of  intersection  is  now  to  be  found  as  a third  pro- 
portional to  ±l,  c and  r (that  is,  the  triangle  ROX  is  to 
be  made  similar  to  LOG),  and  similarly  Y is  a third  pro- 
portional to  L,  s and  R.  (Figure  omitted.)  The  quantity 
x+it  might,  of  course,  be  found  at  once,  as  in  previous 
cases;  but  the  construction  of  the  separate  coordinates 
may  be  more  useful.* 

It  has  now  been  shown  how  to  find  the  intersection  of 
the  circular  locus  by  any  linear  locus  whatever;  a brief 
mention  should  be  made,  however,  of  another  mode  of 
attacking  this  problem,  which  may  be  best  presented  by 
considering  first  the  simpler  one,  to  find  the  point  of  inter- 
section of  two  given  linear  loci.  Suppose  that,  in  each, 
the  two  comitants  zero  are  given  in  position,  also  in  each, 
the  £C-comitant  £ (the  £ having  the  same  value  in  one  as  in 
the  other),  and  in  each,  the  ?/-comitant  fj.  Join  the  inter- 
section of  the  a?-comitants  0 to  that  of  the  accountants  £. 
Now,  since  in  either  locus  the  distances  from  the  accoun- 
tant 0 to  any  two  accountants,  £ and  £',  are  as  the  numbers 
£ and  £■' , it  follows  that  the  line  just  drawn  will  pass 
through  the  intersections  of  any  two  like  accountants  of 
the  two  loci.  So  also  the  line  joining  the  intersection  of 
the  two  ?/-comitants  0 with  that  of  the  ?/-comitants  rj  will 
pass  through  the  intersections  of  all  pairs  of  like  y- comi- 
tants. The  point  in  which  these  two  lines  meet  is  obvi- 
ously the  required  point  of  intersection  of  the  given  linear 
loci. 

The  points  of  intersection  of  any  two  algebraic  loci 
whatever  may  be  determined  by  an  application  of  the 
same  principle;  that  is,  the  curves  which  pass  respec- 
tively through  the  intersections  of  like  accomitants,  and 
through  those  of  like  ^/-comitants  are  always  algebraic 
curves,  whose  equations  result  from  the  elimination  of  £ 
or  of  f]  from  a pair  of  comitant  equations;  and  their  real 
intersections  must  always  correspond  in  position  with  the 
(real  or  imaginary)  intersections  of  the  two  given  loci. 
But  the  application  of  this  method  to  determine  the  inter- 

*The  discussion  of  the  intersections  made  with  a circular  locus  by  imaginary 
radii  leads  directly  to  the  theory  of  the  trigonometric  functions  of  an  imaginary 
variable,  but  this  subject  is  much  too  extensive  to  be  here  entered  upon. 


24 


Colorado  College  Studies. 


sections  of  the  circular  and  linear  locus  is  not  practically 
appropriate,  since  it  invokes  the  aid  of  higher  curves  to 
treat  a problem  which  is  in  fact  amenable  to  the  ruler  and 
compasses.  A similar  objection  must  hold  in  other  cases. 

The  problems  thus  far  considered  embrace  the  con- 
struction of  linear  loci  as  secants,  tangents,  or  polars,  when 
imaginary  quantities  enter  the  problem  in  any  way  what- 
ever; and  are  hence  adaptable  to  the  treatment  of  any 
specific  elementary  question  which  involves  only  one  circle. 
But  there  is  one  particular  case  of  tangents  which,  on  ac- 
count of  its  importance  as  well  as  of  the  special  peculiari- 
ties it  exhibits,  requires  a separate  investigation.  This 
case  is  that  of  the  asymptotes. 

The  equations  of  the  asymptotes  of  the  locus  x2  + y2=?-2 

Y . y 

are  x + iy=0,  or  — =i,  and  x— iy=0,  or— = —i.  It  is  at  once 
5 x ’ x 

apparent  that  the  equation  x + iy=0  for  any  (finite)  values 
of  X and  Y can  be  satisfied  only  at  the  origin;  though  from  the 

Y 

form— =i,  it  appears  that  infinite  values  of  x and  Y might 

x 

differ  numerically  by  any  finite  amount.  Hence  the  finite 
comitants  of  the  locus  all  pass  through  the  origin,  while  any 
line  whatever  of  the  plane  may  be  taken  as  a comitant  in- 
finity. Now  a real  “line  at  infinity”  is  characterized  by 
opposite  properties,  i.  e.,  its  comitants  p,  wdien  p is  any 
finite  quantity,  lie  altogether  in  the  infinitely  distant  region 
of  the  plane,  unless  the  comitant  zero  be  regarded  as 
parallel  to  an  axis,  when  any  other  parallel  to  the  same, 
though  at  a ljnite  distance  therefrom,  becomes  a finite 
comitant.  But  by  assuming  p infinite  we  may  identify  its 
comitants  with  any  lines  in  the  finite  region,  irrespective  of 
direction.  Hence  the  first  “circular  point  at  infinity”  re- 
garded as  the  intersection  of  these  two  loci,  is  at  any  finite 
point;  and  the  statement  that  all  circles  pass  through  this 
one  “circular  point,”  is  only  in  this  sense  true,  that  one 
analytical  expression  will  serve  to  designate  for  all  circles 
the  infinite  coordinates  which  will  satisfy  their  equations; 
while,  as  the  geometric  equivalent  of  this  analytical  ex- 
pression is  indeterminate,  the  point  in  question  is  in  fact 
geometrically  different  for  different  circles.  It  is,  actually, 


The  Circular  Locus. 


25 


in  each  circle,  situated  at  the  center.  Accordingly,  in  ex- 
amining the  intersection  of  x cos  <p-\- Y sin  <p=p  with  the 
locus,  no  indeterminateness  was  found  to  attach  to  the 
position  of  the  interior  point  of  intersection,  when  p was 
increased  indefinitely;  on  the  contrary,  the  limiting  posi- 
tion of  the  intersection  was  found  to  be  the  center  of  the 
circle.  Through  this  point  every  comitant  passes,  and 
each  is  there  touched  by  the  corresponding  comitant  of 
the  asymptote;  while  this  point  of  contact,  in  the  case  of 
a given  comitant — say  the  a?-comitant  (u — has  for  its  coor- 
dinates x=  cc+ifij  y =ix.  It  is  to  be  observed  that  although 
in  this  way  each  single  comitant  exhibits  the  position  of 
the  point  at  infinity,  the  entire  series  of  comitants  can 
illustrate  only  one  form  of  infinite  value  which  might  be 
assigned  to  the  variable  x.  For  beside  the  value  |c 
where  /j.  is  finite,  x might  have  the  infinite  value  oc (x-\-iz) 
with  a finite  ratio  between  x and  £,  or  indeed  it  might  be 
where  x,  the  real  part,  is  finite.  But  in  these  cases 
the  point  of  contact  would  fall  on  a comitant  infinity. 

This  remark  applies  with  still  greater  significance  to  the 
consideration  of  the  second  asymptote,  x— zy=0.  This 
locus  has  nothing  of  the  unique  quality  which  makes  the 
former  asymptote  a correlative  to  the  line  infinity.  Its 
sc-comitant  0 lies  on  the  real  axis  and  its  ?/-comitant  0 on 
the  imaginary  axis,  while  any  comitant  /j.  is  at  a distance 
2 from  the  comitant  zero.  On  the  ^-comitant  /t  the  point 
whose  coordinate  x has  the  value  oc  + ifi  is  at  an  infinite 
distance  from  the  origin;  and  similarly  for  the  ^/-comitants. 
So  long,  then,  as  ;j-  is  finite,  the  point  of  intersection  with 
the  line  infinity  is  represented  by  the  two  points  infinitely 
distant  on  the  two  axes.  Accordingly,  every  (finite)  comi- 
tant of  the  circular  locus  has  for  its  individual  asymptote 
the  corresponding  comitant  of  the  locus  x — ^Y=0.  But  the 
second  circular  point  at  infinity  must  not  on  this  ground 
be  asserted  to  be  represented  only  by  the  infinitely  dis- 
tant points  of  the  axes,  for  if  we  take  into  account  the 
comitants  infinity,  the  direction  of  the  point  in  which  the 
asymptote  locus  meets  the  line  infinity  becomes  indetermi- 
nate; and  this  agrees  with  the  fact  that  the  exterior  inter- 


26 


Colorado  College  Studies. 


section  of  the  line  x cos  ^ + y sin  y=p,  when  p was  made 
infinite,  was  found  to  be  infinitely  distant  on  the  radius 
bounding  the  angle  <p. 

Thus  the  circular  points  at  infinity  are  not  definitely 
localized,  but  it  is  to  be  noted  that  their  indeterminate- 
ness results,  not  from  their  imaginary  quality  alone,  nor 
yet  wholly  from  the  infinity  of  their  coordinates,  but  from 
the  combination  of  both  characters,  and  the  absence  of 
any  means  of  imposing  a definite  value  upon  the  ratio  of 
the  real  and  imaginary  parts. 

The  problems  which  have  been  discussed  in  the  present 
paper  are  mostly  of  the  class  which  relate  to  properties 
of  the  locus  considered  as  a whole,  rather  than  to  those 
of  individual  comitants.  As  such  problems  when  analyzed 
will,  as  a rule,  resolve  themselves  into  investigations  of  the 
intersections  of  the  locus  by  other  loci,  they  will  generally 
be  distinguished  by  the  mark  that  the  comitants  of  the 
two  series  enter  similarly  into  the  geometrical  construc- 
tions; thus  at  the  intersection  of  two  loci  the  like  as-comi- 
tants  and  also  the  like  ?/-comitants  meet  in  the  same  point. 
Of  the  other  class  of  investigations  mentioned,  viz.,  that  in 
which  the  properties  of  individual  comitants  are  the  subject 
of  inquiry,  an  instance  occurs  in  obtaining  the  “ comitant 
equations.”  In  such  problems  it  is  frequently  necessary  to 
employ  separate  symbols  for  the  real  and  imaginary  parts 
of  constants  or  of  variables;  and  if  in  the  subsequent 
course  of  the  investigation,  a symbol  which  has  thus  been 
taken  to  represent  a real  quantity  occurs  as  the  representa- 
tive of  the  unknown  quantity  in  an  equation,  imaginary 
roots  of  such  an  equation  must  of  necessity  be  treated  as 
impossible,  since  they  contradict  the  hypothesis  of  reality. 
This  is  just  as  if  m,  having  been  put  to  represent  the  in- 
tegral part  of  a mixed  number,  in  some  algebraic  problem, 
should  afterward  be  determined  by  a quadratic  equation, 
one  of  whose  roots  should  prove  to  be  integral,  the  other 
fractional.  The  latter  root  would  of  course  be  disregarded, 
without  the  imputation  of  any  unreal  quality  as  belonging 
to  fractions. 


The  Circular  Locus. 


27 


To  illustrate  by  an  example  this  class  of  inquiries,  sup- 
pose that  we  desire  to  determine  at  what  point  a line,  tan- 
gent to  one  of  the  comitants,  cuts  the  same  comitant  again. 
Let  the  accountant  p be  the  curve  in  question,  then  we 
know  that  its  tangent  at  the  point  M,  N (i.  e.,  the  point 
m+i/j;  n+iv,  when  these  quantities  satisfy  the  equation 
M2+N2=r2),  is  the  accountant  p of  the  locus  MX+NY=r2. 
But  the  point  at  which  these  two  lines  again  intersect  will 
not  have  the  same  coordinates,  regarded  as  a point  of  the 
linear  locus,  which  it  has  as  a point  of  the  circular  locus. 
It  is  easily  shown  that  a coincidence  in  position  of  points 
on  two  like  accountants  belonging  to  different  loci,  without 
a concurrent  intersection  of  the  y-comitants,  implies  only 
that  the  real  parts  of  the  coordinates  x for  the  coinciding 
points  differ  by  the  same  amount  as  the  coefficients  of  i in  the 
imaginary  parts  of  their  coordinates  y.  If  we  represent 
this  unknown  difference  by  d,  we  have  the  three  equations 

( x + ip.  )2 + ( y + i'n  Y=r%  ( m-\-ip)2-\-(n+ iv  )2= r2 

and 

(x+ip  + d)  ( m+ip ) -1-  (y  + vq  + id)  ( n+iv)=r 2 

from  which  to  find  x,  y , and  q,  eliminating  d.  Since  each 
of  the  equations  can  be  resolved  into  two,  by  separating 
the  real  and  imaginary  terms,  w’e  can  eliminate  also  two  of 
the  constants,  as  m and  v,  and  find  y in  terms  of  r,  p,  and  n. 
Two  values  of  y will  of  course  be  found  equal  to  n,  and 
represent  the  coincident  intersections  at  the  point  of  con- 
tact, but  the  third,  which  is  the  subject  of  the  inquiry,  is 
determined  by  the  linear  equation 

[ ( pJ— n2 )2 -f  r2p 2 ] y +p  [ ( p2—n2 )2-f-  r\p2— 2 n2 ) ] = 0. 

From  this  value  of  y,  that  of  x and  rj  can  be  found,  and  the 
tangential  point  is  completely  determined.  As  the  equa- 
tion is  linear,  no  trouble  arises  from  imaginaries. 

But  let  it  be  now  required  to  find  on  the  accountant  p 
a point  of  inflection,  using  for  the  purpose  the  property 
that  at  such  a point  the  above-determined  tangential  point 
must  coincide  with  the  point  of  contact.  Then  n is  to  be 
substituted  for  y in  the  above  equation,  and  the  whole 


28 


Colorado  College  Studies. 


solved  for  n.  One  root,  n=ti,  can  be  immediately  found, 
and  this  will  be  seen  to  indicate  the  existence  of  a point  of 
inflection  at  an  infinite  distance.  After  dividing  out  the 
factor  there  remains  the  biquadratic 

n4 + 2 /m3 — 2 ;j-  ( n* + r2 ) n— //  ( /A -f- r2 ) = 0. 

Two  of  the  roots  of  this  equation  are  imaginary,  and  with 
them  a third  must  be  rejected  on  the  ground  that  it  "Cannot 
consist  with  real  values  of  m and  v.  The  remaining  root 
shows  the  position  of  the  two  real,  finite,  points  of  inflec- 
tion. The  three  rejected  roots  are  just  sufficient  in  num- 
ber to  represent  the  six  imaginary  inflections  of  the  cubic 
curve,  whose  real  part  coincides  with  the  ^-comitant 
but  it  seems  plain  that,  consistently  with  the  fundamental 
notions  of  the  present  scheme  of  interpretation,  it  can 
only  be  said  that  the  latter  curve,  considered  as  a comitant 
of  the  locus  x2+Y2=r2,  does  not  possess  these  six  inflec- 
tions. 

As  all  of  the  foregoing  discussion  has  been  limited  to 
the  interpretation  of  the  equation  x2+Y2=r2,  the  circular 
locus  which  has  been  treated  is  not  the  most  general  one 
to  which  the  name  applies,  but  is  merely  the  real  circular 
locus  having  its  center  at  the  origin.  It  seems  proper  in 
a closing  paragraph  or  two,  to  indicate  what  modifications 
of  the  foregoing  constructions  would  result  from  their  ex- 
tension to  the  circular  locus  in  general. 

The  removal  of  the  center  from  the  origin  is  effected 
by  a parallel  transformation  of  coordinates,  in  respect 
to  which  it  is  only  necessary  to  remark  that  transformation 
to  a real  point  simply  changes  the  relative  position  of  the 
axes  in  respect  to  the  entire  system  of  curves,  leaving  the 
latter  unaffected,  while  transformation  to  an  imaginary 
point  disturbs,  not  the  form  of  the  comitant  curves,  but 
the  numbers  by  which  they  are  characterized,  thus  the 
comitant  zero  may  become  the  comitant  fi,  while  some 
other  comitant  of  the  same  series  becomes  the  new  comi- 
tant zero.  From  this  statement,  the  effect  of  such  a change 
on  the  foregoing  geometrical  constructions  may  be  easily 
estimated. 


The  Circular  Locus. 


29 


A more  important  modification  results  from  admitting 
imaginary  values  of  the  radius.  The  equation  x2+y2=r2 
(when  n=r-\-ip),  is  at  once  seen  to  belong  to  a singly  in- 
finite series  of  different  loci,  which  vary  in  form  with  the 
magnitude  of  the  ratio  p : r.  The  case  already  considered 
is  that  in  which  this  ratio  is  zero;  and  the  most  closely 
analogous  case,  as  may  be  readily  conjectured,  is  that  in 
which  the  ratio  is  infinite.  These  two  cases  alone  can  be 
represented  by  equations  with  real  coefficients. 

The  comitants  of  the  locus  x2+Y2+jO2=0,  like  those  of 
x2+Y2=r2,  belonging  to  Newton’s  “defective  hyperbolas 
having  a diameter,”  being  symmetrically  divided  by  one 
of  the  axes.  The  ^c-comitant  0 is  a straight  line,  co- 
inciding with  the  real  axis,  and  the  successive  comitants  £, 
when  £ is  small,  are  conchoidal  curves,  convex  toward  this 
axis,  and  all  touching  it  at  the  origin.  Each  lies  within 
its  predecessor,  and  exhibits  a greater  curvature,  until  the 
a?-comitant  p is  reached,  when  the  curve,  whose  shape  at 
first  might  suggest  a bowl,  and  later  a purse  with  a narrow- 
ing neck,  has  at  length  completely  closed  together,  and  has 
a node  on  the  imaginary  axis,  at  a height  of  p above  the 
origin.  The  succeeding  comitants  have  ovals,  like  the  comi- 
tants of  the  locus  x2+Y2=r2,  but  these  lie  on  the  same 
side  of  the  real  axis  as  the  conchoidal  branches,  and  op- 
posite the  convexity  instead  of  the  concavity  of  the  latter. 
All  the  ovals,  as  in  the  former  case,  touch  the  real  axis  at 
the  origin.  Thus  it  is  seen  that  in  a single  series  of  comi- 
tants occur  successively  representatives  of  Newton’s  species 
45,  41,  and  39 — the  conchoidal  hyperbola  pur  a,  nodata, 
and  cum  ovali,  the  last  having  the  oval  on  the  convex  side. 
As  £ increases  beyond  p to  infinity,  the  conchoidal  branch 
grows  more  straight,  and  the  oval  shrinks  to  a point  at  the 
origin. 

Between  this  form  and  that  of  the  locus  x2+Y2=r2  there 
is  an  unbroken  gradation,  corresponding  to  the  positive 
values  of  the  ratio  p : r ; and  similarly  another  for  the  nega- 
tive values.  In  the  intermediate  forms,  however,  the  comi- 
tants are  no  longer  symmetrical  in  respect  to  either  axis, 


80 


Colokado  College  Studies. 


and  must  be  classed  among  Newton’s  “defective  hyperbolas 
not  having  a diameter.”  The  “comitant  equations”  are 
x*y-\-y3—2Hx*+y*)  + 2?y.x+(p*—r2)y==  0, 
ti3+xy”+2y(x2+y2)  + (p2—  r*)x—  2rp.y=0; 

(and  from  these  as  general  forms  the  special  cases  already 
considered  are  derived  by  making  p or  r equal  to  zero.) 
All  the  comitants  of  a series  pass  through  the  origin,  and 
have  there  a common  tangent.  This  tangent,  however,  for 
the  ^-series,  is  no  longer  the  real  axis,  but  has  a slope  of 

2rp 

— o’  so  that  in  the  loci  in  which  />  = d=r,  the  common 

r — A 

tangent  coincides  with  the  imaginary  axis.  The  infinite 
branches  of  the  comitants  are  not  conchoidal,  but  serpen- 
tine, crossing  their  asymptote  (which  is  still  parallel  to 
the  real  axis,  and  at  a distance  2£  therefrom)  at  a point 

distant  by  -v from  the  imaginary  axis.  In  the  case 

of  the  comitant  zero,  this  crossing  is  at  the  origin,  and  the 
serpentine  curve  is  symmetrical  to  that  point  as  a center, 
thus  belonging  to  the  Newtonian  species  numbered  88.  But 
as  f increases  from  the  value  0,  the  successive  comitants,  no 
longer  possessing  any  kind  of  symmetry,  belong  at  first  to 
the  species  87,  as  they  have  no  oval  and  no  singularity. 
There  is,  however,  the  same  gradual  closing  into  the  form 
of  a narrow-necked  purse,  already  observed  in  the  case 
?"=0,  and  the  comitant  p is  again  nodate,  so  belonging  to 
the  34th  species.  For  still  greater  values  of  c,  the  curve  is 
of  species  33,  having  an  oval,  which,  as  in  all  cases,  shrinks 
to  a point  at  the  origin  as  ? becomes  infinite,  the  serpentine 
branch  in  the  meantime  straightening  toward  coincidence 
with  its  asymptote.  The  node  on  the  ^-comitant  p is  at 
that  point  of  the  locus  for  which  Y=0;  and  it  may  be  re- 
marked, as  true  of  all  forms  of  the  locus,  that  the  four 
points  characterized  by  zero  values  of  one  or  the  other  co- 
ordinate are  double  points  of  the  comitants  of  opposite 
name  on  which  they  fall. 

Yery  slight  and  obvious  modifications  are  alone  required 
to  adapt  the  first  method  given  in  the  present  paper  for  the 
construction  of  comitants,  to  use  with  any  given  values  of 
r and  p. 


ON  THE  EIGHT  LINES  USUALLY  PREFIXED  TO 
HORAT.  SERM.  I.  10.1 


By  WILFRED  F*.  MUSTARD. 


The  eight  lines  usually  prefixed  to  Horace,  Satires, 
I.  10  are  found  only  in  some  of  the  mss.  of  Keller  and 
Holder’s  third  class.  They  are  unknown  to  the  mss.  of 
classes  I and  II,  and  to  0 and  the  whole  family  of 
class  III.  They  were  apparently  unknown  to  the  Scholiasts, 
who  would  surely  have  considered  them  obscure  enough 
to  require  some  explanation.  Mavortius  did  not  know 
them.  In  FA'  and  some  other  mss.  they  appear  as  the  be- 
ginning of  satire  10,  while  in  fi/mp  they  form  a continua- 
tion of  satire  9. 

On  this  external  evidence  almost  all  the  editors  have 
condemned  the  lines  as  an  interpolation,  and  either 
marked  them  off  by  brackets  or  omitted  them  altogether.2 
They  appear  as  part  of  the  text  in  Zarotto’s  Milan  edition, 
in  the  first  and  second  Aldine  editions,  and  in  the  Paris 
edition  by  R.  Stephanus.  But  even  in  the  fifteenth  cen- 
tury Landino  rejected  them,  and  most  of  the  older  editors 
followed  his  example.  Some  editors  have  separated  them 
from  the  text  but  prefixed  them  to  the  satire,  others  have 
printed  them  separately  in  their  commentaries,  while 
many  have  omitted  them  altogether.  Thus  they  do  not 
appear  in  ten  of  the  Venice  editions  (for  the  omission  in 
the  first  eight  Landino  was  responsible),  in  Bentley’s, Wake- 
field’s and  some  twenty  others.  Lambin  ascribes  them  to 
some  ‘ semidoctus  nebulo  ’ who  wished  to  explain  the  open- 

1 This  paper  offers  no  new  theory  as  to  the  meaning,  authorship  or  date  of 
these  obscure  lines.  It  is  merely  an  attempt  to  collect  and  arrange  the  various 
opinions  that  have  been  expressed  with  regard  to  them. 

2 1 owe  the  greater  part  of  the  facts  presented  in  this  and  the  following  para- 
graph to  Kirchner’s  edition  of  the  first  book  of  the  Satires  (Leipzig,  1854),  p.  142. 


32 


Colorado  College  Studies. 


ing  word  ‘nempe.’  Jacobus  Cruquius  barely  mentions 
them  in  his  commentary  as  the  words  of  a ‘simius  Hora- 
tianus.’  Bentley  omits  them  without  mention. 

Others  have  defended  the  lines.  Gesner  restored  them. 
Valart  thought  they  were  the  work  of  Horace.  Heindorf, 
followed  by  Bothe  and  others,  thought  that  Horace  had 
written  them  as  an  introduction  to  this  satire  but  after- 
wards threw  them  aside  and  commenced  in  a different 
tone;  or  that  they  were  an  unfinished  introduction  to  some 
satire  discovered  after  his  death  and,  with  the  addition  of 
the  expletive  words  ‘ut  redeam  illuc,’  prefixed  to  Sat.  I. 
10,  on  account  of  the  similarity  of  subject.  Jo.  Yal. 
Francke  proposed  to  insert  them  after  verse  51  of  this 
satire,  Beisig  after  verse  71.  Morgenstern  held  that  Horace 
had  written  the  lines,  but  afterwards  rejected  them. 
Schmid3  virtually  said  that  they  were  the  work  of  Horace. 
Apitz4  ascribed  them  to  Horace,  but  bracketed  verse  8. 
Urlichs5  said  that  the  old  question  is  really  one  of  sub- 
jective feeling  as  to  what  is  worthy  or  unworthy  of  Horace. 
He  thought  the  lines  genuine,  though  he  admitted  their 
obscurity  and  considered  the  text  corrupt.  Doderlein 
found  nothing  seriously  objectionable  in  the  lines,  and 
was  quite  certain  of  their  genuineness.  He  maintained 
that  tli&  fact  that  they  are  not  found  in  many  mss. 
does  not  prove  them  spurious;  this  might  be  the  result 
of  chance,  or  even  of  a recension  by  Horace  himself. 
W.  Teuffel’s6  verdict  was  similar  to  Morgenstern’s. 

The  text  of  these  obscure  lines  is  very  corrupt.  The 
mss.  of  most  importance  for  determining  the  original 
reading  are  FA'/S'.  F,  the  principal  representative  of  the 
large  third  class,  is  the  assumed  common  source  of  the 
‘ gemelli  Parisini <p  7974  and  <p  7971;  /'  the  archetype  of 
a similar  pair,  k Leidensis  and  1 Parisinus ; /S'  that  of 
/?  Bernensis  and  f Franckeranus  (now  Leeuwardensis) . 

3Philol.  XI.  pp.  54-59. 

4 Coniectan.  in  Q.  H.  F.  Satiras  (Berlin,  1856),  p.  86. 

5 Rhein.  Mus.  XI.  p.  602. 

6 Rhein.  Mus.  XXX.  p.  621. 


Horat.  Serm.  I.  10  (1-8).  33 

These  mss.  agree  very  closely,  and  establish  the  text  as 
follows: 

Lucili,  quam  sis  mendosus,  teste  Catone 

defensore  tuo  pervincam,  qui  male  factos 

emendare  parat  versus,  hoc  lenius  ille 

quo  melior  vir  est,  longe  subtilior  illo 

qui  multum  puer  et  loris  et  funibus  udis 

exoratus,  ut  esset  opem  qui  ferre  poetis 

antiquis  posset  contra  fastidia  nostra, 

grammaticorum  equitum  doctissimus.  ut  redeam  illuc, 

“How  full  of  faults  you  are,  Lucilius,  I shall  clearly 
prove  from  the  testimony  of  Cato,  your  champion,  who  is 
preparing  to  revise  your  ill  made  verses.  He  will  deal 
more  gently  with  them  inasmuch  as  he  is  a better  man,  of 
far  finer  tastes,  than  the  scholar  who  in  his  boyhood  felt 
the  vigorous  persuasion  of  moistened  thong  and  rope,  in 
order  that  there  might  be  one  who  could  lend  a helping 
hand  to  the  poets  of  old  against  the  carping  criticism  of 
our  day,  the  cleverest  of  aristocratic  grammarians.  To  re- 
turn to  that  point,” 


NOTES  ON  THE  TEXT. 

Vs.  1.  ‘quod  sis’  (codd.plerique  ap.  Lamb.).  Some  of 
the  abbreviated  forms  of  ‘quam’  and  ‘quod’  in  minuscular 
writing  are  very  much  alike.7  Unless  very  carefully  written 
these  words  might  be  readily  confused,  and  so  ‘quod’  may 
have  appeared  here.  When  once  it  had  appeared  in  a ms. 
it  might  easily  be  retained  because  of  its  use  in  late  Latin 
to  introduce  substantival  clauses  after  ‘verba  dicendi  et 
sentiendi.8 

Vs.  2.  ‘convincam’  (ed.  Landini  ex  mss.)  for  ‘ pervin- 
cam,’ wThich  as  the  more  difficult  reading  should  be  re- 
tained. One  ms.  ( Kirchneri  cod.  L in  Dresd.  III.)  gives 
‘devincam.’  Peerlkamp  suggested  ‘prope  vincam.’ 

Vs.  4.  ‘quo  melior  vir  est.’  This  is  the  reading  of  the 
most  important  mss.  The  false  quantity  in  ‘vir’  has 


7 Chassant,  Dictionnaire  des  abbreviations , latines  et  francaises,  Paris,  1876,  p.  77, 

8Draeger,  Hist.  Syntax  der  latein.  Sprache , Vol.  II.,  p.  229. 


34 


Colorado  College  Studies. 


given  rise  to  many  attempts  at  improving  the  line.  Thus 
one  ms.  has  ‘quo  vir  melior  est,’  another  ‘quo  vir  est 
melior,’  a third  ‘quo  est  vir  melior,’  while  several  read  ‘est 
quo  vir  melior.’  The  last  arrangement  of  the  words  gives 
undue  emphasis  to  ‘est.’  Lambin  conjectured  ‘quo 
melior  is  est,’  and  the  Martinius  of  Cruquius,  the  only 
one  of  his  mss.  that  contained  these  eight  lines,  had 
‘quo  melior  hie  est.’  But  there  are  pronouns  enough 
already  in  ‘ ille  . . . illo.’  Several  mss.  had  ‘quo  melior  vir 
et  est  longe  subtilior.’  Meineke  defended  this  liyperbaton 
for  ‘quo  melior  vir  est  et  longe  subtilior,’  appealing  to 
Sat.  I.  3,  63;  I.  4,  68;  I.  9,  51.  This,  however,  gives  the 
impossible  combination  ‘quo  longe  subtilior.’  Heindorf 
found  ‘adest’  in  Berol.  5 and  accepted  it. 

Vs.  5.  ‘puer  et.’  The  obscurity  of  this  line  has  given 
rise  to  several  emendations:  ‘puer  est’  (Gesner) ; ‘pueros’ 
(Urlichs);  ‘puerum  est’  (Reisig);  ‘nuper’  (Rutgers); 
‘fuerit’  (Praedicow,  who  also  read  ‘quern’  and  ‘exhorta- 
tus’);  ‘pueros’  (Nipperdey9).  W.  Teuffel10  suggested  ‘me 
olim’  for  ‘multum’  and  defended  ‘olim’  by  a reference  to 
Sat.  I.  4,  105. 

Vs.  6.  ‘exoratus’  is  confirmed  by  the  number  and  im- 
portance of  the  mss.  in  which  it  is  found.  The  other 
mss.  readings  ‘exortatus’  and  ‘exhortatus’  are  only  pos- 
sible with  ‘ puerum  ’ in  the  preceding  line,  for  there  is  very 
little  authority  for  the  active  form  or  passive  meaning  of 
‘exhortor.’  In  any  case  the  omission  of  ‘est’  is  a diffi- 
culty, and  hence,  apparently,  Peerlkamp’s  conjecture  ‘est 
hortatus.’  The  conjectures  ‘exornatus’  (Glareanus)  and 
‘est  ornatus’  (Yalart)  are  obviously  suggested  by  such  ex- 
pressions as  ‘ adeo  exornatum  dabo,  adeo  depexum,  ut  dum 
vivat,  meminerit  mei.’* 11  Horkel  apparently  wanted  a good 
strong  word  after  ‘loris  et  f unibus,’  and  settled  upon  ‘ex- 
coriatus,’  which  Meineke  and  Schiitz  approve. 


9 Opusc.  493. 

10  Rhein.  Mus.  XXX.  p.  622. 

11  Ter.  Heaut.  5, 1,  77. 


Horat.  Serm.  I.  10  (1-8). 


35 


Fss.  4-6.  In  the  Rheinisches  Museum  fur  Philologie, 
XLI.  pp.  552-556,  F.  Marx  offered  the  following  emen- 


dation: 


— hoc  lenius  ille, 


quo  melior  versu  est,  longe  subtilior  illo 
qui  multum  puerum  et  loris  et  funibus  ussit 
exoratus, — 


His  explanation  and  defense  of  these  changes  are  given 
below. 


COMMENTARY. 

In  the  very  first  verse  there  is  evidence  of  the  spurious 
nature  of  this  fragment,  for  (1)  the  promise  ‘quam  sis 
mendosus,  teste  Cat  one,  pervincam’  is  not  fulfilled,  and  (2) 
the  sentiment  is  unlike  Horace.  In  the  tenth  satire  he 
defends  the  opinion  he  had  pronounced  upon  Lucilius  in 
Sat.  I.  4,  but  with  full  recognition  of  his  peculiar  merits, 
and  elsewhere  he  very  modestly  claims  for  himself  a lower 
place  than  for  his  predecessor.12  “To  Lucilius  he  pays  also 
the  sincerer  tribute  of  frequent  imitation.  He  made  him 
his  model,  in  regard  both  to  form  and  substance,  in  his 
satires;  and  even  in  his  epistles  he  still  acknowledges  the 
guidance  of  his  earliest  master.” 13 

‘Teste  Catone.’  The  Cato  here  referred  to  is  the  gram- 
marian Valerius  Cato,  who  is  mentioned  in  Suetonius14  as 
‘poetam  simul  grammaticumque  notissimum,’  ‘summum 
grammaticum  optimum  poetam,’ 4 Cato  grammaticus,  latina 
Siren.’  Another  section  of  Suetonius  tells  of  Cato’s  in- 
terest in  the  works  of  Lucilius,  ‘quas  (sc.  Lucili  saturas) 
legisse  se  apud  Archelaum  Pompeius  Lenaeus,  apud  Pliilo- 
comum  Valerius  Cato  praedicant.’15 

Those  who  see  in  the  person  here  compared  with  Cato 
the  ‘plagosum  Orbilium’  of  Horace,  Epp.  II.  1,  70,  assume 
that  the  writer  of  these  lines  knew  that  epistle,  which  is 

12 Sat.  II.  1,  29,  ‘me  pedibus  delectat  claudere  verba,  Lucili  ritu,  nostrum 
melioris  utroque.’  Ibid.  74,  ‘quicquid  sum  ego,  quamvis  infra  Lucili  censum 
ingeniumque.’ 

13  Sellar,  The  Roman  Poets  of  the  Republic , 3ded.,  1889,  p.  249. 

uDe  Gramm.  4 and  11. 

15  De  Gramm.  2. 


Colorado  College  Studies. 


36 

assigned  by  Vahlen  to  B.  C.  14.  Suetonius,  de  granny.  11, 
says  of  Cato,  ‘vixit  ad  extremam  senectutem,’  so  that 
‘emendare  parat’  might  be  literally  true  if  the  lines  were 
genuine.  Marx  claims  that  the  words  need  mean  only 
‘emendare  studet,  emendationi  operam  dat,  emendaturus 
est,’  comparing  Juv.  8,  130,  ‘per  oppida  curvis  unguibus 
ire  parat  nummos  raptura  Calaeno.’  Moreover,  he  main- 
tains, the  author  of  these  lines  pronounces  upon  the  whole 
recension  of  Cato,  implying  that  it  was  already  finished,  so 
that  they  were  not  necessarily  composed  in  the  time  of 
Horace. 

Keller  objects  even  to  the  sentiment  of  ‘teste  Catone’ 
that  (1).  Horace  required  no  one’s  authority  to  confirm  his 
opinion  of  Lucilius,  and  (2),  in  view  of  Epp.  I.  19,  39-40, 
it  is  not  likely  that  he  would  have  appealed  to  the  author- 
ity of  any  grammarian.16  This  he  regards  as  another  evi- 
dence of  interpolation.  • 

Vs.  3.  Some  editors  punctuate  with  a period  after 
‘versus,1  and  another  after  ‘doctissimus,’  verse  8.  With 
this  punctuation  ‘hoc’  would  most  naturally  be  taken  as 
accusative  after  a finite  verb  understood.  It  seems  better 
to  point  with  commas  and  supply  such  a participle  as 
‘facturus,’  taking  ‘hoc’  as  the  ablative  corresponding  to 
‘quo.’ 

Vs.  4 is  certainly  corrupt. 

(a)  It  is  strange  that  ‘melior’  should  be  given  as  a 
reason  for  ‘lenius.’  It  must  have  been  this  difficulty  that 
gave  rise  to  the  variant  ‘lenior.’  Cato’s  moral  character  is 
not  at  all  concerned.  All  that  is  required  of  him  is  ability 
to  correct  metrical  errors  and  halting  sense  in  Lucilius’ 
verses,  defects  which  had  probably  been  multiplied  even 
in  his  day  by  mistakes  of  the  copyists.  Nor  does  ‘sub- 
tilior’  suit  ‘lenius,’  for  Lucilius’  verses  are  ‘male  facti.’ 

(b)  There  is  a false  quantity  in  ‘vir.’17 

10 ‘non  ego,  nobilium  scriptorum  auditor  et  ultor, 
grammaticas  ambire  tribus  et  pulpita  dignor.’ 

17  The  Italian  dialects  show  that  the  ‘ i ’ in  * vir  ’ was  once  long  ( veir ) : cp. 
Buecheler,  Lex.  Jtal.  p.  30. 


Horat.  Serm.  I.  10  (1-8). 


37 


( c ) ‘ Longe  subtilior’  is  irregular.  “ Cicero  and  the  older 
writers  did  not  use  4 longe  ’ to  strengthen  the  comparative, 
though  it  appears  in  poets  of  a later  age  and  in  the  more 
recent  historians.”18  Wolflinn19  says  that  Horace  kept 
strictly  to  the  old  rule  of  4multo’  with  the  comparative, 
using  ‘longe’  only  in  one  anomalous  case.  He  would 
therefore  not  have  written  ‘longe’  here  instead  of  its  met- 
rical equivalent  ‘multo,’  and  its  use  is  one  proof  of  the 
spurious  nature  of  these  eight  lines. 

(d)  ‘ Ille’  and  ‘ illo,’  ending  consecutive  lines  and  refer- 
ring to  different  persons,  are  strange  and  confusing  as  to 
meaning.  Suetonius  rejected  a certain  prose  epistle  which 
purported  to  have  been  written  by  Horace,  ‘ epistula  etiam 
obscura,  quo  vitio  minime  tenebatur’.20  He  would  scarcely 
have  found  the  transparency  of  genuineness  in  verses  3-4. 
To  avoid  the  difficulties  in  ‘lenius’  and  ‘ille  . . . illo’  Schutz 
would  strike  out  the  two  half- lines  and  read  ‘emendare 
parat  versus  subtilior  illo.” 

Vs.  5.  If  the  genuineness  of  verse  4 may  be  questioned 
on  the  ground  of  obscurity,  still  more  objectionable  is 
verse  5.  It  seems  impossible  to  explain  this  and  the  fol- 
lowing lines  in  their  best  attested  form.  For  example, 
who  is  the  person  compared  with  Cato? 

(a)  Because  Horace  says,  Epp.  II.  1,  70,  that  he  studied 
the  poems  of  Livius  Andronicus  in  his  boyhood  under  the 
‘plagosus  Orbilius,’  many  editors  have  made  ‘qui  puer  . . . 
exoratus’  refer  to  the  poet  himself.  It  may  be  doubted 
whether  Horace  would  have  thus  spoken  of  himself,  but  a 
greater  difficulty  awaits  us  inverse  8,  ‘equitum  doctissimus.’ 
These  words  most  naturally  refer  to  the  same  person  as 
‘qui  . . . exoratus,’  and  Horace  was  not  an  ‘eques.’ 

( b ) Reisig,  who  reads  ‘puerum  . . . exliortatus,’  makes 
‘puerum’  refer  to  Horace,  ‘qui’  to  Orbilius.  But  to  this 
Schutz  objects  that  ‘puerum’  would  be  too  indefinite  with- 
out ‘ istum’  or  ‘ilium.’ 


18  Hand,  Tursellinus,  III.  p.  551. 

19  Comparation,  p.  40. 

20  Horatii  Poetae  Vita. 


38 


Colorado  College  Studies. 


Schmid21  also  read  ‘qui  . . . puerum  . . . exhortatus,’  re- 
ferring ‘qui’  to  Orbilins. 

W.  Teuffel22  refers  ‘puerum’  to  Scribonius  Aphrodisius, 
‘qui’  to  Orbilius.  To  this  also  Schlitz  objects  that  Scri- 
bonius was  ‘Orbili  servus  atque  discipulus,’23  and  that 
‘puerum’  would  not  imply  all  this.  He  might  more  rea- 
sonably have  repeated  his  objection  to  Reisig’s  explanation, 
that  the  unmodified  ‘puerum’  is  too  indefinite. 

These  three  interpretations  are  obviously  based  upon 
the  mention  of  the  ‘plagosus  Orbilius,’  Epp.  II.  1,  70,  and 
they  receive  some  support  from  the  words  ‘ grammaticorum 
equitum  doctissimus,’  in  verse  8.  These  words  naturally 
refer  to  the  same  person  as  the  clause  ‘ qui  . . . puerum  . . . 
exhortatus,’  and  Orbilius  might,  at  least  ironically,  be 
called  a knight.24  There  is,  however,  no  evidence  that  he 
revised  Lucilius’  ‘ ill  made  verses,’  or  that  he  paid  special 
attention  to  them. 

(c)  J.  Becker25  thought  that  either  Florus  or  Titius  is 
meant.  Very  little  is  known  of  these  men  except  from 
Horace,  Epp.  I.  3,  and  II.  2.  Horace  merely  says  that 
Florus  has  ability  enough  to  win  distinction  in  oratory, 
in  law,  or  in  poetry.26  Porphyrio  says  ‘hie  Florus  [scriba] 
fuit  satirarum  scriptor,  cuius  sunt  electae  ex  Ennio, 
Lucilio,  Varrone.’  Kiessling  hints  that  the  old  commen- 
tator inferred  all  this  from  Epp.  I.  3,  21,  ‘quae  circum- 
volitas  agilis  thyma  ? ’ Whether  right  or  not,  Porphyrio 
apparently  means  that  Florus  rewrote  some  of  the  poems 
of  these  earlier  authors,  adapting  them  for  the  readers  of 
his  own  day.  Even  if  this  be  accepted,  it  is  hard  to  sup- 
pose that  Horace  would  refer  to  Florus  in  the  language  of 
these  eight  lines,  and  yet  address  him  fifteen  years  later 
as  a young  man  who  had  not  written  much.27  Of  Titius 
still  less  is  known.  Horace  asks  Florus  whether  he  is  still 


21  Philol.  XI.  pp.  54-59. 

22  Rhein.  Mus.  XXX.  p.  622. 

23Sueton.  Be  Gramm.  19. 

24Sueton.  De  Gramm.  9,  ‘ deinde  in  Macedonia  corniculo,  mox  equo  meruit.’ 

25  Philol.  IV.  p.  490. 

26  Epp.  I.  3,  23-25. 

2i  Epp.  1.3,  22-25. 


Horat.  Serm.  I.  10  (1-8). 


39 


writing  odes  or  trying  his  hand  aidrRgedy,,  vTitius  Romana 
brevi  ventnrus  in  ora.’28  All  that.tFe  scholiast^ -ha to  say 
about  him  may  very  well  have  begn  derived  from  the  text. 
Thus  Becker’s  theory  seems*  ’to-  haye>  v6ry  little  .support, 
except  Porphyrio’s  statement  that.  Floras  w'riter  of 

satires,  and  the  fact  that  Titius  and  Fiorus  were  both 
noblemen  of  a literary  turn,  and  might  be  called  ‘ equitum 
doctissimi.’  That  either  of  them  could  be  called  ‘ gram- 
maticorum  equitum  doctissimus’  is  by  no  means  apparent. 

‘ Loris  et  funibus  udis.’  The  mention  of  dora’  and 
dunes’  suggests  a rather  savage  treatment  of  the  un- 
known youth  referred  to  in  this  line.  References  to  the 
use  of  dunes’  for  the  purpose  of  punishment  are  not  very 
numerous.  Horace,  however,  has  ‘ Hibericis  peruste  funi- 
bus latus,’29  on  which  Orelli  remarks  that  dunes’  made 
from  the  Spanish  broom  were  used  for  flogging  the  ma- 
rines. No  very  satisfactory  explanation  of  the  word  ‘udis’ 
has  ever  been  offered.  It  is  not  clear  that  savage  masters 
sometimes  used  a moistened  lash,  or  that  a lash  so  treated 
would  cause  the  victim  more  pain.  Marx30  quotes  Petro- 
nius,  134  B,  dorum  in  aqua,’  as  inconsistent  with  such  ex- 
planations. It  is  unfortunate  that  the  wisdom  of  the 
scholiasts  was  not  brought  to  bear  upon  this  word;  their 
comments  would  certainly  have  been  interesting. 

Pss.  3-6.  The  changes  in  these  three  lines  suggested  by 
F.  Marx  have  been  mentioned  on  page  35.  First  he  empha- 
sizes the  importance  of  the  word  ‘ exoratus  ’ in  the  interpreta- 
tion of  this  fragment,  a word  which  is  preserved  by  all  the 
best  mss.  of  the  third  class.  This  word,  he  says,  may  here 
be  equivalent  to  dhougli  vainly  implored  for  mercy,’  like 
‘exorata’  in  Juvenal,  6,  415,  ‘vicinos  humiles  rapere  et  con- 
cidere  loris  exorata  solet.’31  Then  reading  ‘puerum’  for 
4 puer,’ 32  as  many  earlier  scholars  have  done,  he  looks  about 

23Epp.  I.  3,9. 

™Epod.  4,  3. 

30  Rhein.  Mus.  XLI.  p.  552. 

31 A similar  use  of  ‘ exorare,’  which  he  might  have  quoted,  is  found  in  Hor. 
Epp.  1. 1,  6,  ‘latet  abditus  agro,  ne  populum  extrema  toties  exoret  harena.’  With 
this  meaning  of  * exoret,’  ‘ toties  ’ may  be  taken  literally. 

32  An  easy  change  paleographically. 


40 


. Colorado  College  Studies. 


for  a finite  verb.Q^ tsfiikmg ’ pr  ‘ cutting.’  This,  he  thinks, 
is  lurking  in  ‘udis,r  which  is  certainly  very  wbak  and  has 
never  been  well  explained.  The  verb  is  probably  ‘ ussit.’ 
It  should  bp  noticed  thatlth*e,  wof*d  ‘udis’  appears  ‘in  r as.  ft? 
and  that  very  bir4tf5n  jin  mss.  the  termination  ‘-it  ’ shows  a 
medial  ‘d.’ 33  For  similar,  uses  of  the  verb  ‘ urere  ’ cp.  Horace, 
Epp.  I.  16,  47,  ‘loris  non  ureris’;  Epod.  4,  3,  ‘Hibericis 
peruste  funibus’;  Sat.  II.  7,  58,  ‘virgis  uri.’  The  conjec- 
ture ‘quo  melior  versu  est’  in  the  fourth  line  he  puts  for- 
ward with  less  confidence. 

Marx  then  refers  his  new  reading,  ‘qui  multum 
puerum  . . . ussit  exoratus,’  to  Vettius  Philocomus,  Cato’s 
teacher,  who  was  one  of  the  first  to  revise  the  work  of 
Lucilius.34  This  man,  as  being  ‘Lucilii  familiaris,’  and 
possibly  the  same  person  who  was  censured  by  the  poet 
‘propter  sermonem  parum  urbanum,’35  may  have  been  like 
Aelius  Stilo  and  Servius  Clodius,  a Roman  knight.  His 
name,  however,  suggests  a Greek  origin,  and  in  the  absence 
of  any  special  statement  as  to  his  rank,  it  is  not  easy  to 
assume  that  he  was  an  ‘eques.’ 

Vs.  8.  The  words  ‘grammaticorum  equitum  doctissi- 
mus’  are  very  difficult  both  in  reference  and  in  meaning. 
They  would  most  naturally  refer  to  the  same  person  as 
‘qui  . . . exoratus,’  but  they  can  hardly  apply  to  the  per- 
son who  is  so  unfavorably  compared  with  Cato.  Schutz 
claims  that  such  irony  as  this  is  quite  impossible  here,  and 
failing  to  find  any  other  person  to  whom  the  epithet  could 
easily  be  referred,  would  strike  out  the  words  altogether. 
Apitz36  bracketed  the  whole  of  verse  8. 

Kirchner  and  Doderlein  would  refer  ‘doctissimus’  to 
the  same  person  as  ‘melior’  and  ‘subtilior,’  i.  e.,  to  Cato. 

33  Examples  of  this  interchange  in  Horatian  mss.  are  cited  by  Keller  and 
Holder,  Epilegom.  III.  p.  853.  A similar  list  is  given  in  Mayor’s  The  Latin  Hepta- 
teuch, p.  251. 

34Sueton.  De  Gramm.  2. 

35  Quint.  Inst.  Or.  I.  5,  56,  taceo  de  tuscis  et  sabinis  et  praenestinis  quoque : 
nam  et  eorum  sermone  utentem  Vettium  (Vectium?)  Lucilius  insectatur,  quem- 
admodum  Pollio  repreliendit  in  Livio  Patavinitatem,  licet  omnia  italica  pro 
romanis  habeam. 

36  Coniectan.  in  Q.  H.  F.  Satiras,  1856,  p.  86. 


Horat.  Serm.  I.  10  (1-8). 


41 


The  long  separation  is  decidedly  against  this,  and,  besides, 
Cato  could  hardly  be  called  an  ‘eques.’  According  to 
Suetonius,  De  Gramm.,  11,  his  social  position  was  doubtful 
in  his  manhood  and  he  probably  never  had  a knight’s  in- 
come in  his  old  age.  To  meet  this  last  difficulty  Kirchner 
proposed  to  read  ‘equidem’  for  ‘equitum.’ 

The  reading  ‘doctissime’  has  been  proposed,  but  this 
is  obviously  suggested  by  the  knowledge  that  Lucilius 
was  a knight,  and  the  objectionable  interval  is  only  in- 
creased. 

The  words  ‘grammaticorum  equitum’  are  especially 
obscure.  As  they  stand  they  would  seem  to  imply  a class 
of  knights  who  were  grammarians,  or  of  grammarians  who 
were  knights,37  but  such  guilds  are  quite  unknown. 

Doderlein  punctuated  with  a comma  after  ‘ grammati- 
corum.’ As  has  been  mentioned  above,  he  considered 
these  eight  verses  the  genuine  introduction  to  Sat.  I.  10, 
so  that  in  trying  to  avoid  one  difficulty  he  created  another 
almost  as  serious,  by  making  Horace  class  himself  among 
the  grammarians — ‘fastidia  nostra  grammaticorum.’38 

Badius  Ascensis  thought  Maecenas  was  the  ‘eques’; 
another  old  scholar  thought  of  Laberius.  Orelli  came  to 
the  conclusion  that  the  writer  of  these  verses,  whoever  he 
was,  knew  no  more  who  the  ‘eques’  was  than  we  do. 

‘Ut  redeam  illuc.’  Cp.  Sat.  I.  1,  108,  ‘illuc,  unde  abii, 
redeo,’  and  Nepos,  Dion.,  4,  ‘sed  illuc  revertor’;  Agesil.  4, 
‘sed  illuc  redeamus.’ 

It  is  hard  to  find  anything  in  the  preceding  lines  to 
which  ‘illuc’  can  well  be  referred.  As  Kruger39  remarks,  it 
cannot  refer  to  the  promised  proof  that  Lucilius  is  full  of 
faults,  for  this  promise  is  not  fulfilled,  or  to  the  proof  of 
his  faults  on  Cato’s  evidence,  for  Horace  does  not  return  to 
this  at  all.  Voss  and  Francke  made  ‘illuc’  refer  in  a gen- 
eral way  to  Sat.  I.  4,  or  its  subject. 

37  Like  Juvenal,  VIII.  49,  nobilis  indocti,  ‘ a nobleman  who  is  an  ignoramus.’ 
38 This  is  contrary  to  the  sentiment  of  Epp.  I.  19,  40,  ‘ non  ego  . . . grammati- 
cas  ambire  tribus  et  pulpita  dignor.’ 

39  Drei  Satiren  fuer  den  Schulzweck  erklaert , 1850,  p.  17. 


42  Colorado  College  Studies. 

i 

It  seems  almost  certain  that  these  three  words  were  in- 
serted on  account  of  the  abrupt  opening,  ‘Nempe  etc.’40 
The  preceding  lines  were  probably  written  with  the  text 
of  Sat.  I.  10  on  account  of  the  similarity  of  subject,  and 
some  later  scribe,  mistaking  them  for  the  introduction  to 
this  satire,  would  add  the  words  ‘ ut  redeam  illuc’  to  serve 
as  a bridge  to  the  lively  opening  ‘Nempe  incomposito  dixi 
etc.,’  though,  as  Schiitz  remarks,  they  would  serve  better  to 
connect  the  verses  with  verse  2,  ‘quis  tarn  Lucili  fautor 
inepte  est?’  The  long  introduction  to  Sat.  I.  7 (followed  by 
‘ad  Begem  redeo,’  vs.  9)  may  have  suggested  the  expletive 
words  that  wore  felt  necessary.  Keller  and  Holder  cite  as 
similar  interpolations  the  four  lines  once  prefixed  to  the 
Aeneid  and  the  ten  lines  at  the  beginning  of  Hesiod’s 
Works  and  Days.  It  is  incontestable,  they  add,  that  the 
satire  is  complete  without  these  eight  verses,  and  that 
nothing  is  wanting  at  the  beginning.  On  the  contrary, 
the  fact  that  Persius,  the  deliberate  imitator  of  Horace, 
begins  one  of  his  satires  (the  third)  with  ‘nempe’  speaks 
for  the  genuineness  of  the  introductory  ‘nempe’  here. 


The  external  evidence  that  these  eight  verses  are  an 
interpolation  to  Sat.  I.  10  is  given  in  the  first  paragraph 
of  this  paper;  a careful  examination  of  them  can  only  re- 
sult in  the  conclusion  that  they  are  not  the  work  of  Horace 
at  all.  They  have  been  assigned  to  different  writers  and 
to  different  periods. 

Kirchner  ascribed  them  to  Furius  Bibaculus  (circ.  700 
A.  U.  C.),  arguing  from  Sueton.  De  Gramm. 11,  that  Valerius 
Cato,  if  still  alive  when  Horace  wrote  this  satire  (A.  U.  C. 
720),  must  have  been  over  seventy  years  old,  too  old  to  be 
contemplating  a revision  of  Lucilius.  This  argument  was 
soon  afterwards  disposed  of  by  Schmid,41  who  proved  from 
the  same  section  of  Suetonius  that  Cato  could  not  have 
been  more  than  sixty-two  years  old  in  A.  U.  C.  720,  and 


40 1 Scil.  ut  transitus  ad  Horatium  sit.’  Baehrens,  Fragm.  Poet.  Roman.,  1886,  p.  329. 
uphilol.X I.  p.  54. 


Horat.  Serm.  I.  10  (1-8). 


43 


was  probably  alive  several  years  later.42  0.  Fr.  Hermann 
ascribed  them  to  Fannius.  Lucian  Muller,  in  his  edition 
of  Lucilius,  1872,  says  they  were  undoubtedly  composed  in 
the  time  of  Horace,  though  their  authorship  is  uncertain. 
These  three  scholars  insisted  on  taking  ‘emendare  parat’ 
literally. 

Schiitz  says  that  the  writer  of  the  fifth  verse  appar- 
ently knew  not  only  Epod.4,  3,  ‘Hibericis  peruste  funibus’ 
and  4,  11,  ‘sectus  flagellis  . . . praeconis  ad  fastidium,’  but 
also  Epp.  II.  1,  70,  ‘plagosum  . . . Orbilium,  etc.’  This 
epistle  is  assigned  by  Vahlen  to  B.  C.  14,  so  that  these 
verses  could  not  have  been  written  by  Fannius  or  by 
Furius  Bibaculus.  He  would  put  the  composition  of  the 
fragment  as  late  at  least  as  the  beginning  of  the  second 
century  A.  D.  Just  as  Tacitus43  says  that  there  are  men 
in  his  day  who  prefer  Lucilius  to  Horace,  and  Quintilian44 
insists  that  Horace’s  criticism  is  unfair,  so  the  unknown 
writer  of  these  lines  objects  to  Horace’s  treatment  of  his 
own  model,  appealing  to  the  authority  of  Cato,  who  was  of 
course  not  satisfied  with  the  work  of  Lucilius  as  he  found 
it,  but  still  thought  it  worth  revising.45  The  third  verse, 
Schiitz  maintains,  is  not  necessarily  older  than  Sueton. 
De  Gramm.  2.  The  writer  may  have,  known  Suetonius’ 
account  of  Cato  and  yet  made  him  an  editor  not  merely  a 
student  of  Cato  in  his  younger  days,  either  by  mistake  or 
because  he  knew  or  thought  he  knew  better. 

Orelli  remarks  that  the  passage  has  ‘antiquum  colorem,’ 
and  assigns  it  to  the  time  of  Fronto.  Keller  would  put  it 
as  late  as  Ausonius  (circ.  350  A.  D.),  hinting  at  Tetra- 
dius  who  is  addressed  in  Auson.  Ep.  15,  9,  as  rivalling 
Lucilius.46 

F.  Marx,  whose  beautiful  emendation  of  these  lines  is 
often  referred  to  in  this  paper,  says  that  they  are  impor- 
tant for  the  history  of  grammar  at  Borne  and  for  our 

42 1 vixit  ad  extremam  senectutem.’ 

43  Dial,  de  Or  at.  23. 

44  Inst.  Or.  X.  1,  93. 

45  It  would  be  hard  to  show  that  Horace’s  estimate  of  Lucilius  was  any  lower 
than  this. 

46  * rudes  Camenas  qui  Suessae  praevenis  aevoque  cedis,  non  stilo.’ 


44 


Colorado  College  Studies. 


knowledge  of  the  fate  of  Lucilius’  poems.  The  whole  pass- 
age, he  insists,  suggests  the  philologist  and  reviewer,  who 
prefers  Cato’s  edition  of  Lucilius  -to  his  master’s  earlier 
one.  There  is  a vast  difference  between  the  points  of  view 
of  Horace  and  the  author  of  these  interpolated  lines:  the 
former  speaks  of  Lucilius  himself  and  his  works,  the  latter 
of  editors  and  editions. 

If  it  once  be  assumed  that  the  words  ‘emendare  parat’ 
do  not  necessarily  imply  that  these  lines  were  written  in 
Cato’s  lifetime,  it  is  hard  to  say  how  late  they  may  have 
been  composed.  Whatever  their  age,  it  is  quite  impossible 
to  name  their  author. 

The  fragment — and  it  is  only  a fragment,  for  the  promise 
in  the  first  verse  is  not  fulfilled — seems  to  have  been  trans- 
ferred to  this  satire  from  some  source  rather  than  composed 
as  an  introduction  to  it,  to  explain  and  complete  it.  Apart 
from  the  fact  that  the  general  sentiment  of  the  lines  (so 
far  as  this  can  be  discovered)  is  not  in  accord  with  that  of 
the  satire  to  which  they  are  unnecessarily  prefixed,  it  is 
hard  to  see  what  Horace  had  to  do  with  Cato’s  alleged  re- 
vision of  Lucilius  or  with  the  savage  treatment  of  the  un- 
fortunate youth  referred  to  in  verse  5.  Keller  and  Holder 
say  that  the  ‘Urliandsclirift’  of  their  third  class  of  mss. 
was  older  than  Priscian,  and  so  also  this  interpolation, 
adding,  however,  that  while  Priscian  quotes  the  spurious 
lines  prefixed  to  the  Aeneid,  these  eight  verses  are  not 
mentioned  by  any  of  the  ancient  commentators. 


STATE  BANK  NOTES. 


By  W.  M.  HALL. 


The  proposal  to  restore  the  privilege  of  note-circulation 
to  banks  outside  of  the  national  bank  system,  by  removing 
the  practically  prohibitory  ten  per  cent,  tax,  is  supported 
chiefly  by  the  following  doctrines: 

I.  That  the  probable  extinction  of  the  national  bank 
circulation  will  leave  a gap  in  the  money-supply  that  must 
be  filled  by  notes  of  some  kind. 

II.  That  a well-guarded  system  of  state  bank  notes 
would  give  us  an  “elastic”  circulation,  i.  e.,  one  that 
would  increase  with  each  high  tide  of  business,  and  con- 
tract when  business  slackened. 

III.  That  state  bank  notes  would  give  a larger  perma- 
nent money-circulation  to  parts  of  the  country  that  are 
now  scantily  supplied  with  money. 

IV.  That  the  present  prohibitory  tax  on  state  bank 
notes  violates  the  spirit  of  the  Constitution  if  not  its  letter, 
and  is  a dangerous  encroachment  upon  State  powers  or 
individual  liberty  or  both. 

I. — NOTES  TO  FILL  A VACANCY. 

The  first  of  these  doctrines  could  be  summarily  dis- 
missed, in  view  of  the  well-known  habits  of  the  interna- 
tional flow  of  gold,  except  so  far  as  the  shrinkage  of  the 
whole  money-supply  of  the  world  would  affect  the  scale  of 
prices  a little;  a shrinkage  that  can  be  avoided  by  other 
means  than  bank  notes.  Yet  the  recent  experience  of  the 
United  States  with  money  is  not  only  an  illustration  of 
the  international  flow,  but  it  is  worth  examination  because 
it  offers  striking  and  encouraging  proof  that  the  substitu- 
tion of  coin  for  national  bank  notes  is  not  likely  to  be  a 
painful  process. 


46 


Colorado  College  Studies. 


From  the  monthly  estimates,  made  by  the  Treasury 
Department  are  taken  the  following  figures,  showing  the 
amount  of  each  kind  of  money  in  circulation  on  July  1 of 
the  year  named.  Money  held  by  the  banks  is  included, 
for  the  stock  they  keep  does  not  far  exceed  (though  it  does 
in  July  somewhat  exceed)  a reasonable  reserve,  which  is  as 
much  a part  of  the  needs  of  ordinary  business  as  is  the 
reserve  of  five  dollars  or  fifty  below  which  the  head  of  a 
family  does  not  permit  his  cash  in  hand  to  fall.  Money  in 
the  Treasury  is  not  included,  because  much  of  it  is  held 
merely  to  redeem  certificates  that  are  circulating  outside; 
and  because  there  has  been  a widely  varying  amount  there, 
the  variations  of  which  had  an  unbusinesslike  origin.  There 
would  be  no  material  difference  in  results,  so  far  as  the  pur- 
pose of  this  paper  is  concerned,  if  the  money  in  the  Treas- 
ury, less  the  backing  of  certificates,  were  included.  The 
figures  in  parentheses  for  the  true  amount  of  national  bank 
notes  are  round  numbers,  estimated  from  the  reports  of  the 
Comptroller  of  the  Currency;  this  needs  to  be  distinguished 
from  the  nominal  amount,  because  notes  of  surrendered 
circulation,  being  no  longer  an  obligation  upon  the  banks 
that  issued  them,  are  really  certificates  payable  by  the 
United  States. 


MONEY  IN  CIRCULATION. 
(Millions  of  dollars.) 


1879 

1882 

1885 

1888 

1890 

1892 

Gold*  (including  Gold  Certificates) . . 

126 

363 

468 

512 

505 

550 

Silver  Dollars  (including  Certificates) 

9 

87 

141 

256 

360 

384 

Greenbacks  and  Legal  Tender  Certif. 

302 

325 

331 

308 

335 

342 

Notes  of  1890 

98 

National  Bank  Notes,  nominally 

321 

352 

309 

245 

182 

167 

(National  Bank  Notes,  really) 

(310) 

(315) 

(270) 

(155) 

(125) 

(140) 

Subsidiary  Silver 

67 

52 

44 

50 

54 

62 

Totals 

825 

1,179 

1,293 

1,371 

1,436 

1,603 

[Copper  and  nickel  coins  are  disregarded ; so  is  paper  fractional  currency, 
which  was  reckoned  about'  16  millions  in  1879  and  only  about  7 millions  since, 
including  the  amount  in  the  Treasury.  The  figures  of  subsidiary  silver  for  1879 
and  1882  are  too  large,  through  including  trade  dollars.] 


* The  figures  for  gold,  after  1879,  are  often  disputed  as  too  large ; and  prob- 
ably with  good  reason.  But  it  will  be  seen  ( page  56)  that  allowance  for  a smaller 
amount  does  not  vitiate  the  conclusions  of  this  paper. 


State  Bank  Notes. 


47 


It  may  here  be  seen  clearly  how  the  whole  volume  of 
money  has  responded  to  the  needs  of  increased  business; 
the  growth  was  rapid  in  the  revival  of  business  following 
1879,  and  then  fell  to  a much  lower  rate,  averaging  little 
over  30  millions  annually  from  1882  to  1890.  But  the  fact 
which  now  most  concerns  us  is  that  the  needs  of  business 
were  not  provided  for  by  the  creation  of  bank  notes,  nor 
of  any  kind  of  notes,  except  the  note-element  in  the  silver 
dollars  and  the  notes  of  1890,  and  a small  increase  in  the 
greenbacks  outside  of  the  Treasury.  More  than  that,  the 
nominal  bank-note  circulation  was  reduced  in  the  thirteen 
years  by  154  millions,  and  the  true  bank-note  circulation 
by  about  170  millions.  If  1882  and  1892  be  compared,  the 
reduction  in  the  ten  years  is  185  or  175  millions;  a reduc- 
tion greater  than  the  amount  now  outstanding.  That  is, 
we  have  only  to  do  once  more  just  what  we  have  done  since 
1882,  and  the  whole  of  the  national  bank  notes  will  be  re- 
placed by  other  money. 

But  the  matter  is  not  quite  so  simple,  because  we  shall 
not  do  just  what  we  have  done  since  1882.  The  effect  of 
the  Act  of  1890  needs  to  be  considered,  and  the  effect  of  a 
possible  repeal  of  that  Act.  Before  weighing  these,  it  is 
desirable  to  look  closely  at  the  nature  of  the  past  additions 
to  the  money-supply,  in  respect  to  their  real  cost.  Their 
cost  to  the  country  is  measured  approximately  by  the  export 
value  which  the  gold  and  silver  would  have  had  if  not  used 
for  money  purposes  here.  The  cost  of  coinage  and  storage, 
and  other  such  minor  corrections,  may  be  disregarded,  in 
view  of  the  wide  allowance  for  error  that  will  be  used  in 
the  inquiry,  and  of  the  unequivocal  result.  Of  course  the 
government  purchases  have  steadily  “bulled”  the  silver 
market;  how  much,  it  is  not  possible  to  know.  Against 
whatever  such  enhancement  of  the  price  of  silver  there 
has  been,  acting  as  a diminution  of  the  cost  to  the  country 
(not  the  government  only)  of  the  silver  used  for  money, 
there  is  a partial  offset  in  the  increase  of  cost  to  the  country 
of  all  its  money-metal,  through  the  necessity  of  making 
slightly  lower  average  prices  for  exported  goods  in  order 


48 


Colorado  College.  Studies. 


to  send  them  out  in  place  of  the  metal  withheld  and  thus 
maintain  the  equilibrium  of  foreign  trade.  But  to  put  the 
result  of  the  inquiry  beyond  suspicion,  it  may  be  prudent 
to  allow  for  the  one  conspicuous  effect  through  enhance- 
ment of  price  of  silver;  and  figures  taken  both  with  and 
without  that  allowance  will  be  limits  between  which  the 
truth  lies. 

Evidently  we  must  include  in  the  cost  not  only  the  im- 
ported metal,  but  the  metal  produced  here,  so  far  as  either 
has  been  used  for  money.  And  for  this  purpose  we  may 
better  allow  for  the  Treasury  holdings  also,  because  if 
there  is  an  increase  of  metal  there  the  country  has  bought 
it  by  exporting  goods  or  by  abstaining  from  importing 
them.  The  increase  in  gold  used  for  money,  either  out- 
right or  through  certificates,  represents  one  large  part  of 
our  expenditure  to  procure  new  money.  The  other  large 
part  is  represented  by  the  gold- value  for  export*  of  the 
silver  in  the  added  silver  dollars,  plus  the  silver  bought  by 
notes  of  1890.  The  supply  of  silver  dollars  in  the  middle  of 
1879,  including  the  Treasury  stock,  was  41  millions;  in  1882, 
123  millions;  in  1892,  414  millions.  In  the  figures  for  1879 
and  1882  are  counted  several  millions  of  silver  bullion, 
destined  soon  to  become  dollars;  the  much  larger  amount 
of  silver  bullion  in  1892,  and  the  much  wider  divergence 
of  its  coinage-value  and  cost-price,  are  cause  for  consider- 
ing it  separately  below.  The  increase  from  1879  to  1882 
was  82  millions,  which  cost  the  government  as  bullion 
about  72  millions;  the  international  market  value  was  a 
little  less,  but  we  may  neglect  the  error.  The  silver  that 
made  the  increase  of  291  millions  of  silver  dollars,  1882  to 
1892,  was  substantially  all  bought  by  the  middle  of  1891; 
it  cost  the  government  about  230  millions.  Using  this 
purchase-cost  as  the  upper  limit  of  what  the  silver  really 
cost  the  country,  we  have  yet  to  fix  the  lower  limit  sug- 
gested above.  Higher  price  of  silver,  caused  by  govern- 
ment buying,  affects  for  this  purpose  not  only  the  silver 
thus  withheld  from  export,  but  the  silver  still  exported. 

* This  is  the  export-value  from  time  to  time ; not  the  present  export-value  of 
the  accumulated  mass. 


State  Bank  Notes. 


49 


The  change  of  price  in  silver  that  would  in  any  case  have 
been  used  at  home  does  not  sensibly  affect  the  cost,  being 
a mere  readjustment  of  domestic  exchanges.  The  correc- 
tion applies,  then,  to  the  silver  bought  by  government, 
added  to  the  net  silver-export  still  remaining  (which  may 
be  a positive  or  negative  quantity;  the  latter  representing 
an  import  and  consequent  loss  by  the  raised  price).  The 
net  export  of  silver  from  1879  to  1892  was  worth  about 
$100,000,000;  from  1882  to  1892,  about  $80,000,000.  The 
government  purchases  from  1879  to  1890  were  about  a 
quarter  of  the  world’s  product,  and  since  1890  more  than 
a third,  and  their  effect  on  the  price  must  have  been  con- 
siderable; but  it  seems  liberal  to  set  three-quarters  of  the 
actual  price  as  the  lower  limit  of  the  price  as  it  might  have 
been  with  no  government  purchases  except  for  subsidiary 
coinage.  On  that  scale,  the  goods  received  in  exchange  for 
the  exported  silver*  of  1879-92  may,  at  the  lower  limit, 
have  cost  the  country  $25,000,000  less  than  their  apparent 
cost;  for  the  exported  silver  of  1882-92,  $20,000,000  less. 
Any  such  gain  diminishes  the  cost  of  our  use  of  silver  for 
money,  and  corresponding  deductions  are  incorporated  in 
the  following  table,  where  the  cost  of  the  silver  bought  by 
the  Treasury  appears  separately,  with  the  same  three- 
quarters  rule  used  to  deduce  a lower  limit  of  true  cost. 


COST  TO  THE  COUNTRY,  IN  GOLD. 
(Millions  of  dollars.) 


1879-92 

1882-92 

Lower 

limit. 

Upper 

limit. 

Lower 

limit. 

Upper 

limit. 

Increase  of  Silver  Dollars,  373  millions 

226 

302 

Increase  of  Silver  Dollars,  291  millions 

172 

230 

Silver  bought  with  1890  notes,  and  not  coined 

58 

77 

58 

77 

Deduction  for  enhanced  value  of  silver  exported 

—25 

—20 

Increase  of  Goldf 

418 

418 

157 

157 

Whole  cost 

677 

797 

367 

464 

Average  cost  per  year 

52 

61 

37 

46(4 

* It  would  be  a needless  refinement  of  the  question  to  take  account  of  the 
diminished  home  production  and  export,  due  to  lower  price. 

f Including  gold  coin  and  bullion  held  by  the  Treasury.  The  official  estimate 
is  246  miHions  in  1879,  507  in  1882,  664  in  1892. 


50  Colorado  College  Studies. 

That  is  to  say,  the  country  has  given  full  value  in  goods 
and  labor  for  somewhere  between  677  and  797  millions  of 
its  increase  of  money-supply  since  1879;  and  for  between 
367  and  464  millions  of  the  increase  since  1882. 

The  money-supply  itself,  outside  of  the  Treasury,  in- 
creased by  778  millions  from  1879  to  1892  (see  table,  p.  46); 
but  the  decrease  of  national  bank  notes  caused  the  increase 
of  the  other  elements  of  the  currency  to  be  still  larger. 
Gold  increased  424  millions,  silver  dollars  375  millions, 
“greenbacks”  40  millions,  and  98  millions  of  1890  notes 
were  added;  making  an  increase,  aside  from  national  bank 
notes  and  pieces  less  than  one  dollar  (which  last  would 
have  shown  about  the  same  behavior  under  any  system  of 
major  currency),  of  937  millions.  This  last  is  the  amount 
of  money  that  has  been  added  in  thirteen  years  past  to 
meet  the  needs  of  increased  business  and  take  the  place  of 
the  declining  bank  note  circulation.  But  we  have  seen 
that  the  country  earned  meanwhile,  i.  e.,  bought  with 
goods  and  labor  for  which  it  received  nothing  else  in 
exchange,  between  677  and  797  millions.*  That  is,  the 
note-elementf  in  the  addition  of  937  millions  was  between 
140  and  260  millions.  If  1882  and  1892  be  compared,  the 
whole  addition  of  money  other  than  national  bank  notes 
and  small  pieces  will  appear  as  599  millions,  and  the  note- 


* This  comparison  of  increase  of  money-supply  outside  the  Treasury  with 
increase  of  money-metal  both  within  and  without  the  Treasury  may  seem  irra- 
tional. But  the  former  is  the  true  measure  of  past  additions  to  the  money-supply 
and  the  better  basis  for  judging  what  future  additions  are  probable,  and  hence 
what  the  strain  of  making  them  will  be ; while  the  sacrifice  in  former  acquisi- 
tions is  better  measured  by  the  addition  of  metal  in  Treasury  and  outside  circu- 
lation together.  If  any  one  nevertheless  prefers  to  compare  outside  circulation 
in  both  cases,  he  will  find  the  increase  of  silver  dollars  (table,  p.  46)  from  1879  to 
1892  to  be  375  millions,  1890  notes  98  millions,  gold  424  millions,  and  the  resulting 
“ lower  and  upper  limits  ” about  700  and  825  millions  ; differing  from  the  677  and 
797  millions,  reckoned  above,  in  the  direction  of  decreasing  the  note-element  in 
past  acquisitions,  and  therefore  of  decreasing  the  sacrifice  needed  in  future  acqui- 
sitions that  may  contain  a less  note-element  or  none  at  all.  That  is,  it  would 
strengthen  the  conclusion  that  in  the  text  above  is  based  upon  a less  favorable 
supposition. 

fNot  the  note-element  reckoned  upon  the  present  bullion  value  of  silver, 
but  the  unearned  part  of  the  issues  of  silver  dollars  and  1890  notes  as  they  were 
made. 


State  Bank  Notes. 


51 


element  as  between  135  and  232  millions.  The  following 
figures  show,  accordingly,  the  average  annual  addition: 

Whole  addition.  Note-element. 

( Millions.) 

Annually,  1879  to  1892 72  Between  11  and  20 

Annually,  1882  to  1892 60  Between  1314  and  23 

And  the  country  has  earned  (see,  also,  the  table  on  p.  49) 
between  52  and  61  millions  annually  through  the  longer 
period,  and  between  37  and  46^  millions  annually  through 
the  shorter. 

It  may  safely  be  said  that  our  probable  dealing  with 
silver  in  the  next  few  years  (omitting  free  coinage  as  too 
improbable  in  the  immediate  future  to  justify  the  discus- 
sion, necessarily  long,  of  its  bearing  on  the  present  ques- 
tion) will  lie  within  a range  bounded  by — 

(1)  Continuance  of  the  Act  of  1890. 

(2)  Revival  of  the  Act  of  1878. 

(3)  Purchase  of  silver,  and  issue  of  notes  whose 
silver  backing,  reckoned  as  bullion,  is  kept  equal  to 
the  face  value  of  the  notes;  kept  equal  by  subsequent 
purchase  of  silver,  if  necessary,  without  issue  of 
notes  against  the  supplementary  silver. 

(4)  Suspension  of  silver  purchases,  except  for 
small  coins. 

It  is  quite  possible  that  silver  legislation  may  combine 
two  of  these  methods,  or  change  the  amount  of  silver  to 
be  bought  under  (1)  or  (2).  But  the  present  object  is  to 
discover  whether  the  national  sacrifice  in  obtaining  addi- 
tional money  will  be  greater  hereafter  than  it  has  been  for 
a few  years  past,  and  that  object  will  be  sufficiently 
attained  by  taking  each  method  separately  and  noting  the 
effect  in  (1),  (2)  and  (3)  of  different  amounts  of  silver- 
purchase;  for  any  combination  will  be  more  favorable  than 
the  least  favorable  method  standing  alone. 

( 1. ) Continuance  of  the  Act  of  1890.  If  this  happens, 
the  addition  of  money  will  be  wholly  earned,  except  for  the 
“lower  limit”  purpose  a note-element  due  to  the  higher 
price  of  the  silver  bought  and  the  silver  exported.  The 


52 


Colorado  College  Studies. 


silver  bought  is  54  million  ounces  annually,  which  is  sub- 
stantially the  whole  amount  available  for  Treasury  pur- 
chase or  export.*  The  domestic  production  of  silver  is 
increasing  by  about  4 million  ounces  per  year;  but  sup- 
posing (to  keep  on  the  less  favorable  side  of  probabilityf ) 
that  the  amount  exported  in  the  next  dozen  years  should 
average  only  6 million  ounces,  while  54  millions  were  still 
bought,  the  amount  through  which  the  higher  price  could 
operate  to  diminish  the  true  cost  would  be  about  60 
million  ounces  annually ; worth  $60,000,000  at  one  dollar, 
$45,000,000  at  75  cents.  Accordingly  the  note-element,  on 
the  three-quarters  scale,  lies  between  zero  and  15  millions 
in  the  improbable  event  of  a rise  of  silver  that  carried  it 
to  average  $1  an  ounce,  between  zero  and  11  millions  if 
silver  averaged  75  cents.  A smaller  government  purchase 
would  not  change  the  quantity  of  silver  affected,  but  it 
would  of  course  bring  the  note-element  nearer  to  the  zero 
limit  through  affecting  the  price  less. 

( 2. ) Revival  of  the  Act  of  1878.  Taking  its  minimum 
purchase  of  $24,000,000  worth  of  silver  annually,  the  dol- 
lars coined  would  be,  with  silver  at  $1  an  ounce,  31  mil- 
lions; with  silver  at  75  cents,  41  millions.  The  seigniorage 
would  thus  be  7 and  17  millions  at  those  prices  respectively. 
The  other  part  of  the  note-element,  by  the  three-quarters 
rule,  would  be  (as  under  the  Act  of  1890)  between  zero  and 
15  millions  at  the  former  price,  between  zero  and  11  mil- 
lions at  the  latter.  The  whole  note-element  is  thus  between 
7 and  22  millions  when  silver  is  at  one  dollar  an  ounce, 
between  17  and  28  millions  at  75  cents.  Evidently  the 
note-element  is  enlarged  by  increased  purchases  or  by  a 
fall  of  silver. 

(3.)  Issue  of  notes  with  a constantly  equivalent  silver 
hacking ; a backing  kept  equivalent,  when  the  price  of  silver 
declines,  by  purchase  of  more  silver  without  issue  of  notes 

* The  net  import  was  about  3 millions  in  the  fiscal  year  1891 ; net  export  6 
millions  in  1892. 

t A larger  supposed  export  would  increase  the  note-element  and  decrease  the 
sacrifice. 


State  Bank  Notes. 


53 


against  it.  The  question,  highly  important  for  other  pur- 
poses, whether  the  notes  are  redeemable  in  gold  or  in  a gold 
dollar’s  worth  of  silver,  has  no  bearing  on  this  discussion. 
In  either  case  the  note-element  is  between  zero  and  a quarter 
of  the  export-price  of  60  million  ounces,  minus  the  cost  of 
silver  bought  in  case  of  falling  price  to  keep  up  the  backing 
of  notes  issued  earlier  — that  kind  of  purchase  being  cost 
without  addition  to  the  money-supply.  It  would  be  an 
extreme  supposition  that  silver  should  fall  to  60  cents  an 
ounce  in  the  next  ten  years;  that  would  be  about  2^  cents 
annually.  Such  a fall  would  require,  if  the  annual  pur- 
chase for  note-issue  were  $24,000,000,  a purchase  of  sup- 
plementary silver  amounting  to  less  than  a million  dollars 
in  the  first  year,  to  10  millions  in  the  last  year,  but  averag- 
ing about  5 millions  annually  through  the  ten  years;  while 
the  note-element  due  to  upholding  the  price  of  silver  would 
average  (with  silver  at  an  average  of  72  cents)  between 
zero  and  11  millions.  Deducting  the  5 millions  of  cost  for 
supplements,  we  have  minus  5 and  plus  6 millions  as  the 
limits  of  the  note-element;  that  is,  it  might  possibly  be  a 
more  expensive  way  of  obtaining  new  money  than  import- 
ing gold  would  be.*  On  the  less  extreme  supposition  of  a 
fall  of  silver  to  70  cents  in  ten  years,  the  average  annual 
supplementary  purchase  (the  principal  purchase  being  still 
24  millions)  would  be  something  less  than  3 millions,  mak- 
ing the  note-element  somewhere  between  minus  3 and  plus 
9 millions.f  The  increased  expense,  in  the  later  years,  of 
maintaining  such  a note-system  in  case  of  a progressive 
fall  of  silver  is  of  course  a serious  objection  to  the  system, 
unless  it  is  believed  that  silver  will  not  continue  to  fall. 
If  silver  does  not  change  in  price,  the  note-element  is  the 
same  as  under  the  Act  of  1890;  with  silver  at  84  cents,  it 
is  between  zero  and  12^  millions.  Greater  purchases  would 

*A  loss  of  this  kind,  payable  in  future,  has  already  been  incurred  by  the 
country  through  its  large  purchase  of  silver,  if  silver  does  not  rise  again,  and  if 
the  notes  of  1890  or  silver  dollars  are  ever  given  a 100  per  cent,  backing  or  are 
withdrawn  and  the  silver  sold. 

f Silver  then  averages  about  77  cents,  and  the  note-element,  aside  from  cost 
of  supplements,  is  between  zero  and  lll/2  millions. 


54 


Colorado  College  Studies. 


probably  increase  the  note-element  unless  silver  declined 
2 cents  or  more  yearly. 

(4.)  Suspension  of  silver  purchases,  except  for  small 
coins . This  would  leave  the  natural  movement  of  gold  to 
make  the  necessary  increase  of  money,  and  would  provide 
no  note-element. 

Tabulating  the  effects  of  these  methods  of  dealing  with 
silver,  we  have  the  note-element  appearing  as  follows: 


NOTE-ELEMENT  LIES 
BETWEEN— 


EFFECT  UPON  THE 
NOTE-ELEMENT— 


Method  (l),withActof  ’90  unchanged; 

silver  at  100 

Method  (1)  ,with  Act  of  ’90  unchanged; 

silver  at  75 

Method  (2),  with  annual  purchase 

$24,000,000 ; silver  at  100 

Method  (2),  with  annual  purchase 

$24,000,000 ; silver  at  75 

Method  (3),  with  annual  purchase 
(for  note  issue)  $24,000,000 ; silver 

declining  2*4  cents  yearly 

Method  (3),  with  purchase  24  mill. ; 

silver  declining  1*4  cents 

Method  (3),  with  purchase  24  mill. ; 

no  decline  of  silver 

Method  (4) 


0 

and 

15 

mill.  1 

of  increased 
purchases. 

of  cheaper 
silver. 

0 

and 

11 

mill.  ) 

Increase. 

Decrease. 

7 

and 

22 

mill.  ) 

Increase. 

Increase. 

17 

and 

28 

mill.  ) 

-5 

and 

+6 

mill.* 

Uncertain. 

Decrease. 

-3 

and 

+9 

mill.* 

Uncertain. 

Decrease. 

0 

and 

12*4 

mill. 

Increase. 

Decrease. 

No  note-element. 

The  past  annual  increase  of  the  whole  money-supply, 
together  with  the  money  that  replaced  bank  notes,  has  in- 
cluded a note-element  lying  somewhere  between  11  and  23 
millions  (see  page  51).  If  we  continue  to  extinguish  bank 
notes  at  the  same  rate,  make  no  change  in  the  amount  of 
greenbacks,  and  increase  the  whole  money-supply  at  the 
same  rate  as  before,  it  appears  from  the  table  above  that 
Method  (2)  would  involve  no  appreciable  decrease,  per- 
haps an  increase,  in  the  note-element;  that  is,  the  money 
to  serve  the  growing  needs  of  trade  and  to  take  the  place 
of  disappearing  notes  would  cost  us  not  appreciably  more, 
perhaps  less,  than  it  has  in  the  recent  past.  Under  Method 
(1)  the  national  expense  on  this  score  would  be  say  8 to  12 
millions  more,  annually,  than  it  has  been  in  the  recent  past. 

* For  ten  years  only,  and  as  an  average ; the  note-element  being  less  than 
zero  in  the  later  years,  and  going  further  below  after  the  ten  years,  if  the  fall  of 
silver  continued  at  anything  like  the  same  rate. 


State  Bank  Notes. 


55 


Under  Method  (4)  it  would  be  between  10  and  20  millions 
more.  Under  Method  (3)  it  might  in  a very  unfavorable 
case  be  20  millions  more,  but  with  a slower  decline  of 
silver  the  added  expense  would  be  nearer  the  12  millions  or 
so  (between  10  and  15)  wdiich  would  accompany  a stationary 
price  of  silver.  Under  Method  (3 ) this  average  cost  through 
ten  years  represents  a smaller  cost  in  the  earlier  years  and 
a heavier  one  in  the  later  years,  if  silver  falls.  It  is  only 
under  Method  (3)  that  we  have  to  anticipate  a cost,  for 
the  average  annual  addition  of  money  and  extinction  of 
bank  notes,  exceeding  by  more  than  about  15  millions  the 
cost  that  has  already  become  habitual.  Method  (3),  if 
silver  should  fall  rapidly,  would  be  burdensome  after  a few 
years,  particularly  if  the  annual  issue  of  notes  were  much 
more  than  the  24  millions  reckoned  in  the  table;  but  no 
one  wishes  to  see  that  method  adopted  if  silver  is  to  fall 
rapidly;  and  in  any  case,  the  extinction  of  bank  notes 
within  a dozen  years  would  contribute  only  12  or  14  mil- 
lions annually  to  the  burden.  Under  any  of  the  more  prob- 
able forms  of  dealing  with  silver  the  sacrifice  of  the  country, 
in  extinguishing  the  bank  notes  while  it  increased  the 
whole  circulation,  as  usual,  would  not  exceed  by  more  than 
about  15  millions  the  sacrifice  that  is  already  customary; 
and  it  might  not  exceed  that  at  all.  Remembering  that  in 
place  of  an  annual  cost  of  between  40  and  60  millions  for 
the  near  future,  which  has  been  the  implied  basis  of  the 
present  reckoning  because  it  was  the  average  cost  for  the 
past  few  years  (see  page  49),  we  might  have  for  a part  of 
the  time,  as  in  1879-82,  a cost  of  100  millions  attended  by 
great  commercial  prosperity — remembering,  too,  that  it 
takes  more  than  an  occasional  waste  of  20  or  30  millions 
by  Congress  to  make  an  appreciable  difference  in  the  course 
of  business  — it  seems  unlikely  that  the  withdrawal  of  all 
the  national  bank  notes  within  ten  years  can  give  a sensi- 
ble check  to  business.  Indeed,  the  greatest  expense  for 
new  money  comes  just  at  the  time  when  the  country  can 
best  afford  it,  in  times  of  rapid  growth  of  business;  and 
just  at  the  time  when  there  is  need  of  a check  upon  excessive 
speculation. 


56 


Colorado  College  Studies. 


The  conclusion  just  reached  has  so  wide  a margin  of 
safety  that  it  excuses  the  omission,  for  simplicity’s  sake,  of 
a number  of  corrections;  some  offset  each  other,  some  are 
mere  differences  of  degree  of  an  element  common  to  all  the 
years  (e.g.  a deduction  from  the  probably  excessive  Treasury 
estimate  of  gold  coin  in  private  hands),  and  the  aggregate 
of  the  corrections  can  scarcely  swell  the  difference  between 
past  and  future  sacrifice  in  the  enlargement  of  the  money- 
supply  so  as  to  call  for  the  retention  of  national  bank 
notes,  or  for  the  provision  of  any  other  notes  to  take  their 
place.  If  there  is  any  need  for  state  bank  notes,  it  is  to  be 
found  elsewhere. 


II.— ELASTICITY. 

In  popular  discussion  of  the  repeal  of  the  bank-note 
tax  it  is  often  assumed,  as  something  near  an  axiom,  that 
a bank  note  system  may  readily  be  made  “ elastic,”  and  it 
seems  to  be  implied  that  the  easier  it  is  for  banks  to  issue 
notes  the  more  elastic  the  resulting  currency  will  be.  But 
among  economists  this  is  so  far  from  being  a generally 
accepted  truth  that  some  reputable  writers  deny  the  pos- 
sibility of  bank  notes  following  the  needs  of  trade,  either  in 
expansion  or  contraction  ( except  in  the  same  way  that  coin 
would  have  done),  so  long  as  the  bank  notes  are  really 
convertible,  i.  e.  are  promptly  and  willingly  redeemed  by 
the  bank.  If  nevertheless  we  grant  that  an  expansion  is 
possible,  it  is  reckless  to  assume,  without  careful  examina- 
tion, that  the  bank-note  currency  would  contract  again  when 
trade  slackened.  And  unless  it  does  so  contract,  what  we 
have  is  not  elasticity  but  a wholly  inelastic  distensibility. 

Entering  first  a protest  against  another  too  easy  assump- 
tion, that  elasticity  is  an  unmixed  good  (for  much  may  be 
said  for  the  doctrine  that  the  evil  in  it  exceeds  the  good, 
through  removing  one  of  the  barriers  against  speculative 
excitement),  we  have  to  inquire  what  are  the  causes  that 
may  limit  a note-circulation,  and  whether  any  action  of  the 
State  governments  upon  those  causes  can  give  an  increase 


State  Bank  Notes. 


57 


or  an  elasticity  that  the  National  government  cannot  give 
by  similar  action. 

A bank  issues  notes  in  order  to  increase  its  receipts  of 
interest.  In  a country  where  notes  are  familiar,  it  can 
usually  carry  notes  with  a reserve  smaller  than  that  which 
it  needs  to  carry  deposits*;  and  accordingly,  unless  taxes 
or  other  expenses  intervene,  its  loans  that  can  be  made 
through  notes  are  more  profitable  than  its  loans  through 
book-credits  of  deposit.  But  in  the  United  States  most 
borrowers  prefer  book- credits,  and  the  practicable  note- 
issue  is  restricted  to  so  much  as  can  be  paid  out,  whether 
in  loans  or  in  other  money-payments  (e.p.upon  checks  pre- 
sented), without  coming  back  for  redemption  faster  than 
it  is  reissued.  Within  that  limit  (beyond  it,  if  bank  notes 
were  not  convertible)  the  bank  has  a motive  for  keeping 
its  circulation  as  large  as  possible,  unless  other  expenses 
or  hindrances  appear.  In  the  United  States  the  limit  so 
set  would  be  narrow  for  the  individual  bank,  on  account 
of  the  large  proportion  of  credit-transactions,  except  for 
the  habitually  long  life  of  the  circulating  notes;  in  fact  it 
is  so  wide  that  a limit  for  the  whole  note-circulation,  drawn 
on  the  same  scale,  would  be  impossibly  large.  The  real 
limit  for  the  whole  note-circulation  is  of  course  much  lower, 
because  as  the  whole  amount  approached  a point  consid- 
ered to  be  dangerous,  redemptions  would  become  more  fre- 
quent, i.  e.  the  limit  for  individual  banks  would  shrink. 
Banks  do  not  grow  weary  of  making  a profit,  nor  stop  issu- 
ing notes  without  a reason  for  stopping.  Where  the  note- 
circulation  falls  short  of  the  limit  (usually  wide,  when 
banks  are  well  managed)  set  by  the  return  of  notes  for  re- 
demption, it  is  certain  that  there  are  definite  causes  for  it, 
either  prohibiting  the  increase  of  circulation  or  offsetting 
the  profit  by  some  expense,  inconvenience  or  dread  of  in- 
jury. Including  redemption,  we  may  name  the  following 
restraints  upon  the  issue  of  notes,  some  of  which  are 


* Strictly  speaking,  deposits  which  are  caused  directly  or  indirectly  by  the 
bank’s  loans.  Other  deposits  have  no  bearing  on  the  question  whether  loans  by 
book-credit  or  by  notes  are  more  profitable. 


58  Colorado  College  Studies. 

found  at  work  in  every  bank-note  system,  no  matter  how 
bad: 

checks  upon  the  issue  of  bank  notes. 

1.  Return  of  notes  for  redemption.  The  effect  of  this 
important  restraint  has  been  outlined  above.  It  is  thor- 
oughly effectual  only  when  redemption  is  enforced  by  law 
and  not  discouraged  by  public  opinion  or  by  bank  pressure 
( e . g.  refusing  discounts  and  other  bank  services  to  persons 
w7ho  have  presented  notes  for  redemption ) . But  as  we  shall 
see  hereafter,  unless  certain  artificial  means  are  used  to 
compel  the  return  of  the  notes  within  a given  time,  the 
action  of  this  check  does  not  prevent  an  increase  from  year 
to  year  till  the  issue  is  very  large,  if  public  confidence  in 
the  soundness  of  the  banks  prevails. 

2.  Fear  of  discredit.  That  is,  a belief  of  the  bank 
managers  that  further  issue  of  its  notes  would  impair  the 
bank’s  credit,  and  either  directly  fail  of  its  purpose  by 
bringing  back  for  redemption  notes  equal  to  the  new  issue, 
or  injure  the  deposits  and  other  business  of  the  bank. 

3.  Fear  of  general  injury  to  business.  This  may  in- 
clude one  or  more  of  the  following  elements:  Fear  of  the 
effect  on  the  bank’s  own  business  of  a general  derangement 
of  business  caused  by  bad  currency;  fear  of  the  effect  of 
such  derangement  on  the  interests  of  the  managers  outside 
the  bank;  and  a sense  of  responsibility  and  trusteeship 
towards  the  business  community.  This  check  is  seen  at 
its  best  where  a single  large  bank  issues  most  of  the  bank 
notes  of  a country  (the  circulation  of  notes  of  other  banks 
being  prevented  or  kept  within  narrow  limits  bylaw);  the 
Bank  of  England,  for  instance,  would  doubtless  be  tem- 
perate in  the  issue  of  notes,  even  if  it  were  not  hindered 
by  law  from  making  any  profit  by  an  increase  of  circula- 
tion. The  Bank  of  France  is  influenced  by  a similar  com- 
bined responsibility  and  prudence.  But  when  there  are 
many  banks,  each  knows  that  its  own  note-issue  will  be 
only  a small  part  of  the  whole  note-circulation,  and  that 
its  own  abstention  from  new  issues  will  have  little  effect 


State  Bank  Notes. 


59 


towards  reducing  the  whole;  perhaps  no  effect  at  all,  be- 
cause other  banks  will  issue  more  instead  before  the  more 
rapid  return  for  redemption  comes  into  play,  or  the  legal 
maximum,  if  any,  is  reached.  And  if  some  banks  are  still 
conservative  when  the  motive  to  be  so  is  thus  diminished, 
other  banks  will  surely,  in  such  a country  as  the  United 
States,  be  more  tempted  by  the  profit  than  deterred  by  the 
possible  future  evil,  which  is  made  scarcely  more  probable 
by  their  venture;  unless,  indeed,  the  number  and  character 
of  the  banks  be  so  limited  by  law  that  a joint  agreement  is 
practicable  (a  case  which  will  be  mentioned  below).  The 
point  is,  that  we  cannot  look  to  this  check,  unless  supple- 
mented by  an  agreement  among  the  banks,  to  prevent  an  im- 
mediate increase  of  bank  circulation  if  the  latter  were  made 
otherwise  profitable;  for  some  banks  would  surely  grasp 
at  the  profit. 

4.  I^egal  limitation  of  the  number  of  note-issuing  banks, 
either  by  requiring  a special  legislative  charter  for  each, 
or  by  imposing  onerous  conditions  for  going  into  business 
under  general  law.  This  check  acts  upon  a part  of  the 
field  only,  of  course;  leaving  the  banks  which  come  within 
the  privilege  free  to  increase  circulation,  except  so  far  as 
other  checks  interfere. 

5.  A legal  maximum  of  bank  note  circulation.  This, 
if  set  low  enough,  is  perfect  insurance  against  an  undesir- 
able enlargement.  Evidently,  however,  it  allows  no  “elas- 
ticity ” beyond  the  maximum,  and  does  nothing  to  prevent 
the  circulation  rising  to  near  the  maximum,  so  that  further 
elasticity  is  impossible  unless  that  begins  by  decrease; 
and  the  decrease  must  then  be  due  to  other  checks,  and 
not  to  this,  unless  the  maximum  itself  is  made  different  for 
different  times  of  year. 

6.  A legal  minimum  of  reserve  or  of  securities.  So 
far  as  this  minimum  is  greater  than  the  amount  of  reserve 
or  of  securities  which  the  banks  would  hold  of  their  own 
accord,  it  is  a check  upon  circulation  by  reducing  the  profit. 
In  our  national  banks  it  takes  the  form  of  an  amount  of 


60 


Colorado  College  Studies. 


bonds  costing  much  more  than  the  reserve  that  the  banks 
would  voluntarily  hold,  with  only  partial  compensation  for 
the  difference  in  the  low  interest  received  on  the  bonds. 

7.  Taxes  on  circulation;  another  mode  of  reducing  the 
profit.  Under  the  present  national  bank  law,  not  only 
does  the  tax  on  the  notes  of  outside  banks  extinguish  the 
profit  and  prevent  their  issue,  but  the  tax  upon  national 
banks  of  o neper  cent,  on  circulation  contributes  materially 
to  the  well-known  unprofitableness  to  many  of  them  of  their 
notes. 

8.  Legal  requirements  hampering  the  ready  circula- 
tion of  notes.  For  instance,  that  they  shall  be  of  large 
denominations  only,  that  they  shall  bear  interest  (this 
cuts  into  the  profit  also),  or  that  they  shall  be  of  cumbrous 
size.  Requirements  that  they  should  be  indorsed  on  pass- 
ing, that  they  should  be  on  some  easily  damaged  kind  of 
paper,  that  they  should  be  presented  for  redemption  within 
a certain  time  or  lose  part  of  their  face  value,  would  have 
similar  effect. 

9.  Agreement  among  hanks  to  set  limits  similar  to  5 , 6 
and  8.  In  view  of  the  number  of  American  banks  and  the 
difficulty  of  making  and  enforcing  such  an  agreement,  it 
would  be  a waste  of  time  to  discuss  this  as  a possible  check 
upon  future  issues  here;  at  least  till  it  is  seriously  proposed 
to  have  a few  large  banks  monopolize  the  bank-note  issue. 

Depreciation  may  in  times  of  inconvertibility  act  as  a 
check  upon  issue,  but  no  one  now  proposes  to  have  a sys- 
tem subject  to  enough  depreciation  to  come  within  the 
range  of  that  check.  Another  check,  now  practically  out 
of  the  field,  probably  acted  upon  the  bank-note  circulation 
in  America  early  in  the  century:  scarcity  of  capital  and 
high  rewards  for  its  use  in  other  ways  than  banking.  Some 
men  who  might  have  been  attracted  by  the  high  returns  of 
bank-note  issue  were  still  more  attracted  by  other  enter- 
prises that  would  employ  their  time  so  fully  as  to  make 
inconvenient  the  attempt  to  conduct  a bank. 

Turning  back  now  to  see  what  are  the  checks  that  keep 
our  national  bank  note  circulation  comparatively  small, 


State  Bank  Notes. 


61 


we  observe  at  once  that  the  checks  numbered  2,  8,  5 and  9 
have  no  effect  upon  it.  There  is  no  fear  by  any  bank  that 
its  credit  would  suffer  by  issuing  notes  up  to  the  amount 
permitted  by  law  in  view  of  its  capital,  no  fear  of  general 
injury  to  business  by  the  issue  of  another  hundred  millions 
or  two*,  no  legal  maximum  of  circulation,  no  agreement 
among  the  banks.  Under  No.  8 the  omission  to  make  the 
notes  a general  legal  tender  does  not  in  practice  restrict 
their  circulation,  nor  would  the  banks  issue  any  more  notes 
if  they  were  still  permitted  to  use  denominations  less  than 
five  dollars;  the  exclusion  of  bank  notes  from  the  legal 
reserve  of  national  banks  acts  towards  encouraging  the 
return  of  the  notes  for  redemption,  thus  setting  at  work 
check  No.  1.  Contrariwise,  the  law  has  by  its  assimilation 
of  bank  notes  to  government  notes,  in  size  and  general 
aspect,  done  a little  towards  promoting  their  ready  circula- 
tion. No.  4,  legal  limitation  of  the  number  of  note-issuing 
banks,  appears  in  the  form  of  “onerous  conditions,”  such 
as  a minimum  of  capital,  government  inspection,  prohibi- 
tion of  real-estate  loans  and  of  all  loans  beyond  a certain 
multiple  of  the  reserve  held;  but  this  is  more  than  off- 
set, on  the  whole,  by  the  advantage  which  national  banks 
receive  in  public  opinion  of  their  probable  soundness, 
and  it  would  not  prevent  an  increase  of  note-circulation 
if  such  circulation  offered  a profit.  We  have  left,  therefore, 
the  checks  numbered  1,  6 and  7 ; deducting  No.  1,  which  is 
not  a limit  but  a drag  upon  increase  (making  it  slower 
without  stopping  it),  the  true  causes  of  the  smallness  of 
the  circulation  are  in  Nos.  6 and  7,  i.  e.,  (a)  the  require- 
ment of  deposit  of  bonds  whose  market  value  is  much 
higher  than  the  amount  of  notes  issued  against  them, 
bonds  which  bear  a lower  interest  than  the  bank’s  ordi- 
nary business  yields  and  most  of  which  depreciate  (through 
the  effect  of  the  approach  of  maturity  upon  their  premium) 

* Provided  it  were  gradual,  and  the  annual  purchases  of  silver  by  the  Treasury 
were  small.  If  brought  face  to  face  with  the  possibility  of  a large  increase  of 
bank  notes  not  so  guarded,  banks  would  doubtless  recognize  the  danger;  but, 
as  suggested  under  No.  3 above,  only  a part  of  the  banks  would  probably  hold 
back  from  issue. 


62 


Colorado  College  Studies. 


before  the  bank  can  sell  them,  (6)  the  small  deposit  of  cash 
for  redemption  purposes  at  Washington,  (c)  the  one  per 
cent,  tax  on  the  average  note-circulation  of  the  bank  * 
From  many  banks  these  take  more  than  the  whole  profit 
of  the  notes,  and  the  banks  tolerate  the  loss  as  a sort  of 
advertising  expense,  in  order  to  keep  the  advantage  of 
being  known  to  be  under  government  inspection.  The 
decline  of  the  note-circulation  before  1890  shows  that  on 
the  average  the  loss  exceeded  all  the  gains,  including  the 
advertisement,  and  the  slight  increase  f since  1890  shows 
that  for  two  years  past  the  gains  have  by  a very  narrow 
margin  exceeded  the  loss,  taking  all  banks  together.  The 
failure  of  the  note-circulation  to  be  elastic  is  due  to  the 
expense  and  trouble  of  buying  and  depositing  bonds  to 
secure  the  temporary  addition,  and  withdrawing  and  sell- 
ing the  bonds  when  the  time  for  contraction  comes.  Unless 
the  bonds  are  withdrawn,  the  bank  has  no  motive  to  with- 
draw the  added  notes. 

Since  our  note-circulation  is  now  kept  small  by  the  un- 
profitableness to  the  banks  of  further  increase  (except  the 
trifling  present  increase,  which  may  at  any  time  fade  out 
by  disappearance  of  the  narrow  margin  of  gain  which 
causes  it)  the  way  to  make  room  for  either  elasticity  or 
permanent  increase  is  to  remove  part  at  least  of  the  causes 
of  the  unprofitableness;  to  relax  the  checks  called  6 and  7 
above.  Public  attention  seems  to  be  given  to  the  proposal 
to  abolish  the  ten  per  cent,  national  tax  on  state  bank  cir- 
culation; but  room  for  increase  may  be  had  just  as  cer- 
tainly, though  not  for  so  great  an  increase,  by  reducing  or 
removing  the  one  per  cent,  tax  on  national  bank  circulation, 
or  reducing  the  required  deposit  of  bonds,  or  permitting 
the  substitution  of  other  securities  bearing  higher  interest. 

* Minor  expenses  (like  examiner’s  fees),  so  far  as  they  are  independent  of  the 
amount  of  circulation,  may  better  be  included  under  No.  4 ; and  some  which  vary 
with  the  amount,  such  as  the  cost  of  redemption  and  reissue,  are  small  enough 
to  be  neglected  in  this  article. 

t Increase  in  the  true  circulation.  Notes  of  abandoned  circulation,  awaiting 
redemption  by  the  Treasury,  have  no  place  in  such  a comparison  as  this ; though 
the  government  reports  of  circulating  money  include  them  in  the  figures  of  bank 
notes,  which  thus  deceptively  show  a decrease  since  1890. 


State  Bank  Notes. 


63 


It  would  take  little  change  of  these  restraints  to  cause  a 
marked^ acceleration  of  the  increase  of  national  banknotes 
that  is  even  now  visible.  National  banks  are  as  ready  as 
any  others  to  increase  their  circulation  when  the  increase 
pays. 

IMPERFECT  CONTRACTION. 

Now  let  us  postpone  all  the  difficulties  of  securing  a 
sound  state  bank  currency,  and  suppose  that  either  by 
adopting  a system  of  lightly  taxed  state  bank  notes  or  by 
loosening  the  restrictions  upon  national  banks  we  make 
possible  the  issue  of  100  millions  more  of  secure  bank 
notes.  There  is  no  way  of  making  the  issue  possible  but 
by  making  it  profitable.  If  the  checks  were  so  lessened 
as  to  let  the  profit  exceed  them  before  the  harvest-season* 
came,  there  is  good  reason  to  believe  that  a part  of  the 
extra  notes  thus  made  possible  would  not  only  be  sent  out 
but  kept  out  without  waiting  for  the  crop-season,  unless 
certain  legal  requirements,  hitherto  unusual,  were  imposed 
upon  the  banks  or  certain  new  conditions  attached  to  the 
notes.  If  this  occurred  long  enough  before  the  crop-season 
to  permit  the  swelling  of  the  currency  to  affect  the  amount 
of  coin  (either  by  increasing  export  or  diminishing  import 
of  money-metal),  it  would  to  that  extent  merely  substitute 
notes  for  coin  lost;  the  remainder  of  the  “slack”  would  be 
taken  up  by  the  growth  of  business  at  the  crop-season,  and 
this  remainder  only  would  have  any  value  towards  giving 
elasticity,  the  former  part  being  a needless  and  ( if  extensive 
or  often  repeated)  an  injurious  enlargement  of  the  bank- 
note circulation. 

But  we  will  take  a case  more  favorable  to  the  proposal 
of  a bank  note  elasticity,  and  suppose  no  such  wasted  ele- 
ment in  the  new  issue;  suppose  the  checks  to  be  so  skill- 
fully balanced  against  the  profit  that  the  latter  does  not 
emerge  superior  till  the  rate  of  short-time  interest  rises  at 
harvest-time.  The  new  notes  then  go  out,  and  the  first 
half  of  elasticity  is  thus  displayed.  But  what  assurance 

*For  simplicity,  the  autumnal  moving  of  the  crops  is  spoken  of  alone,  here 
and  later  in  the  discussion ; but  the  same  arguments  apply  to  the  spring  trade 
and  to  sporadic  maxima  of  business. 


64 


Colorado  College  Studies. 


have  we  that  when  the  crop-season  is  past  the  excess  of 
notes  will  be  redeemed  and  disappear  ? The  apparent  answer 
is  that  with  slackening  of  business  the  currency  will  be 
redundant,  bank  reserves  will  be  overstocked,  and  the  banks 
will  have  no  profitable  use  for  the  excess  of  notes,  so  that 
redemptions  will  exceed  reissues  till  the  whole  redundancy 
is  withdrawn.  But  this  is  only  an  apparent  answer.  The 
redundancy  after  the  crop  season  is  not  identical  with  the 
preceding  increase  of  notes;  it  may  be  far  less;  it  usually 
would  be  far  less  in  the  United  States.  The  growth  of  use 
for  money  at  crop-moving  time  is  in  this  country  a mere 
wave  in  an  ascending  slope,  a slope  ascending  so  rapidly 
that  we  seldom  add  less  than  20  millions  a year  to  our 
stock  of  money,  and  sometimes  100  millions;  the  use  is 
never,  except  through  unusual  business  depression,  so 
low  after  the  wave  as  before  it.  Almost  always,  there- 
fore, if  we  provided  elasticity  by  means  of  bank  notes 
unattended  by  special  appliances  for  forcing  their  sub- 
sequent withdrawal,  and  if  the  elasticity  were  wholly 
by  bank  notes  and  no  increase  of  coin  shared  in  it,  the  re- 
dundancy of  money  after  the  crop-season  would  be  less 
than  the  increase  of  notes  during  the  crop-season.  Con- 
ceding that  notes  equivalent  to  the  whole  redundancy  were 
redeemed  and  retired,  what  motive  would  the  banks  have 
for  retiring  the  rest  of  the  recently  added  notes?  Reserves 
have  sunk  to  their  normal  size,  for  that  is  what  the  disap- 
pearance of  redundancy  means;  the  banks  have  no  more 
money  than  they  want  to  use.  As  fast  as  notes  are  re- 
deemed, it  is  then  the  bank’s  interest  to  reissue  them,  i.  e. 
to  use  the  notes  in  place  of  the  money  paid  out  in  redeem- 
ing them.  There  is  thus  a part  of  the  recently  added 
note-supply  that  will  remain  in  circulation.  This  process 
would  be  repeated  at  each  maximum  of  business,  and  ac- 
cordingly, without  such  special  devices  as  will  presently 
be  mentioned,  an  elasticity  provided  by  bank  notes  alone 
would  cause  an  increase  of  the  bank  note  currency  from 
year  to  year. 

But  it  may  be  that  a part  of  the  increase  of  money  at 
crop-moving  time  is  in  coin.  By  taking  the  effect  of  the 


State  Bank  Notes. 


65 


mixture  upon  a period  of  several  years  as  a whole,  we  may 
eliminate  the  causes  of  complication  and  find  a practical 
certainty  that  the  note-circulation  would  show  a progres- 
sive increase.  For  all  the  effects  upon  the  coin-supply 
that  the  occasional  presence  of  more  notes  can  have  are 
upon  one  side,  in  the  direction  of  making  the  coin-supply 
less  than  it  would  otherwise  have  been.  The  issue  of  more 
notes  at  the  crop-season  will  check  the  rise  of  short-time 
interest  and  make  money  easier;  in  fact,  that  is  what  it  is 
intended  for.  Easier  money  means  a better  maintenance 
of  prices  of  goods,  and  consequently  less  encouragement 
of  purchases  here  by  foreign  buyers  and  less  tendency  to 
start  an  import  of  gold  or  a diminution  of  its  export.  In 
short,  the  pressure  at  the  crop-season,  so  far  as  it  is  now 
relieved  by  any  retention  or  import  of  gold,  would  force 
less  relief  of  that  kind  because  the  pressure  itself  would 
be  less.  This,  in  turn,  is  only  a part  of  the  more  general 
statement  that  whenever  there  is  any  change  in  our  money- 
stock  of  gold,  the  presence  of  recently  added  bank  notes 
in  the  circulation  tends  to  make  the  increase  of  gold  less 
or  the  decrease  more  than  it  would  otherwise  have  been; 
for  if  any  given  quantity  of  these  bank  notes  had  been  ab- 
sent, the  tightness  of  the  money-market  would  have  been 
increased  or  its  plethora  diminished.  Taking  any  period 
of  years,  we  may  rely  upon  it  that  effects  of  this  kind  will 
have  happened  while  the  extra  bank  notes  of  the  crop- 
season  were  afloat,  in  which  case  bank  notes  will  have  taken 
the  place  of  the  coin  expelled.  And  these  changes  will  be 
cumulative,  because  the  presence  of  bank  notes  always  acts 
on  that  side  when  it  acts  at  all. 

MEANS  OF  ENFORCING  CONTRACTION. 

The  importance  of  this  practical  certainty  that  the  bank 
note  supply  will  increase  from  year  to  year  if  the  checks 
are  so  balanced  against  profit  as  to  permit  an  easy  increase 
of  notes  at  every  maximum  of  business,  and  if  no  special 
devices  are  used  to  force  all  the  new  notes  back  when  busi- 
ness slackens,  lies  in  its  strongly  commending  to  us  the 
use  of  such  special  devices  if  we  undertake  to  make  an 


66  Colorado  College  Studies. 

elastic  note-circulation.  That  a progressive  increase  of 
notes  is,  on  the  whole,  an  evil,  most  economists  will  agree. 
It  is  true  that  there  is  a gain  by  use  of  cheap  money  when 
it  is  good  money;  that  is,  by  the  less  sacrifice  of  goods 
involved  in  obtaining  it,  the  relative  diminution  of  the 
earned  part  and  increase  of  the  note-part.  But  that  seems 
to  be  more  than  offset  by  the  risks  that  attend  a steady 
increase  of  bank  note  money — sometimes  a distant  risk 
of  an  amount  great  enough  to  be  depreciated,  always 
a risk  of  corruption  of  popular  judgment  about  money 
through  suggestion  of  government  paper  as  a resource 
at  the  first  pinch,  and  usually  an  enhancement  (through 
enlarging  the  number  of  issuing  banks  and  spreading  the 
habit  of  extra  note-issues)  of  the  greater  risk  of  encourag- 
ing riotous  speculation  that  attends  all  schemes  for  elas- 
ticity by  bank  notes. 

As  a special  device  to  keep  an  elastic  note-circulation 
from  increasing  progressively,  the  ingenious  suggestion  of 
the  late  John  Jay  Knox  * may  be  considered  first:  that  the 
notes  added  at  times  of  increase  should  be  of  a different 
color  from  the  others,  and  should  bear  interest  after  a cer- 
tain date.  This  proposal  takes  advantage  of  the  well  known 
fact  that  notes  bearing  interest  will  not  circulate  as  money 
except  when  money  is  very  scarce;  the  holders  naturally 
treat  them  as  a sort  of  bond  instead.  Mr.  Knox’s  species 
of  notes  would,  accordingly,  almost  all  drop  out  of  circula- 
tion as  money  soon  after  the  date  when  interest  was  to 
begin.  If  the  notes  bore  a low  rate  of  interest,  they  would 
find  their  way  to  the  issuing  bank  before  long;  if  a high 
rate,  part  of  them  would  be  kept  by  the  holders  as  an  in- 
vestment. In  the  case  of  a high  rate,  indeed,  the  disappear- 
ance from  circulation  would  begin  before  the  date  arrived, 
and  perhaps  so  soon  as  to  impair  the  intended  elasticity  of 
the  note-circulation. 

While  trusting  to  the  behavior  of  the  note-holders  is 
reasonably  safe,  it  seems  simpler  and  more  certainly  effect- 
ual in  every  case  to  provide  a legal  limit  acting  directly 


* See  the  Forum , February,  1892. 


State  Bank  Notes. 


67 

upon  the  banks.  Suppose,  for  instance,  that  the  increase 
of  the  ordinary  note-circulation  is  prevented  by  fixing  a 
maximum  for  it  as  nearly  as  possible  at  the  point  where  it 
now  is,  admitting  hereafter  no  new  issue  of  notes  on  the 
ordinary  terms,  except  in  place  of  such  circulation  with- 
drawn;* and  that  extra  circulation  be  permitted  on  some 
such  terms  as  these — the  extra  notes  to  be  issued  only  dur- 
ing two  or  three  specified  months  just  before  and  during 
the  crop-season,  and  the  whole  circulation  of  the  bank  to 
be  reduced  to  its  former  dimensions  by,  say,  January  15 
following.  The  reduction,  or  its  equivalent,  may  be  made 
certain  by  requiring  from  the  bank  a deposit  of  money  on 
January  15  in  place  of  any  excess  of  notes  still  outstand- 
ing; the  government  either  to  undertake  the  subsequent 
redemption  itself,  or  to  return  the  money  to  the  bank  as 
fast  as  the  redemption  proceeded.  The  money  being  kept 
idle  by  the  government  meanwhile,  the  effect  on  the  money- 
supply  of  the  country  is  the  same  as  if  the  excess  of  notes 
had  been  wholly  retired  before  January  15;  and  the  con- 
traction has  begun  some  time  before  the  date,  as  the  bank, 
besides  its  actual  redemption,  began  to  accumulate  money 
for  the  final  alternative  redemption  or  deposit  with  the 
government.  The  extra  notes  could  then  have  precisely 
the  same  appearance  as  the  ordinary  notes,  and  have  the 
same  validity  as  between  the  bank  and  the  holder;  it  would 
make  no  difference  whether  the  notes  redeemed  and  re- 
tired were  the  same  individual  notes  that  went  out  in  the 
extra  issue;  all  that  is  necessary  is  the  retirement  of  a 
certain  amount  of  the  notes  of  that  bank,  drawn  indiffer- 
ently from  the  old  and  the  new  ones.  The  whole  matter 
would  be  settled  between  the  government  and  the  bank, 
and  no  one  else  would  be  troubled  with  any  discrimination 
among  the  notes  he  handles.  A second  period  of  possible 
issue  may  be  provided  for  the  “spring  trade”;  but  there 
should  be  at  least  one  space  of  a month  or  two  in  each 

* Giving  preference  to  newly  organized  banks  in  allotting  this  substituted 
ordinary  circulation;  if  any  were  left,  old  banks  that  wished  to  enlarge  their 
ordinary  circulation  could  have  it. 


68 


Colorado  College  Studies. 


year,  and  better  two  such  spaces,  when  the  extra  circula- 
tion is  wholly  absent,  so  that  it  may  have  no  opportunity 
to  become  permanent  circulation  and  displace  coin.*  The 
hard-and-fast  limiting  of  the  ordinary  note-circulation 
need  not  exclude  new  banks  from  the  privilege  of  note- 
issue,  for  if  there  are  not  enough  old  banks  withdrawing 
ordinary  circulation  to  make  room  for  them  in  the  ordinary 
circulation,  the  new  banks  may  nevertheless,  by  coming 
under  the  inspection-rules,  be  allowed  to  share  in  the  extra 
issues. 

The  question  how  the  extra  notes  should  be  secured  is 
of  some  importance.  If  deposit  of  securities  is  required, 
it  will  be  found  to  impair  the  readiness  of  the  banks  to 
issue  extra  notes;  the  nearer  the  formality  and  expense  of 
making  the  issue  approached  that  of  the  ordinary  issue, 
the  less  elasticity  the  system  would  give.  On  the  other 
hand,  if  the  original  security  were  no  more  than  enough 
for  the  ordinary  issue,  it  would  not  be  enough  for  a per- 
fect safeguard  to  the  increased  amount.f  A first  claim 
upon  all  the  property  of  the  bank,  reinforced  by  a safety 
fund  and  perhaps  by  a personal  liability  of  the  stock- 
holders, would  be  very  strong,  but  might  imaginably  fail 
in  some  one  or  two  instances  at  last;  though  the  govern- 
ment might  protect  the  note-holder  by  assuming  that  risk 
itself  through  guarantying  the  notes,  or  transfer  it  to  the 
other  banks  in  the  system  through  making  them  respon- 
sible beyond  their  share  of  the  safety  fund.  All  these 
comments  upon  the  mode  of  securing  the  notes'  apply 
equally  to  Mr.  Knox’s  plan  and  to  the  second  plan  de- 
scribed. Bo  do  all  the  following  questions:  What  securi- 
ties should  take  the  place  of  United  States  bonds  when 
those  are  extinct;  whether  a maximum  should  be  set  to  the 

* I.  e.  displace  coin  progressively.  There  would  doubtless  be  a slight  dis- 
placement in  the  first  year  or  two,  and  then  the  coin-supply  would  go  on  a little 
less  than  it  would  otherwise  have  been,  but  less  by  a nearly  constant  amount. 

t But  the  deposit  of  securities  for  the  ordinary  circulation  might  be  made  to 
exceed  the  face-value  of  the  ordinary  notes  by  a margin  large  enough  to  cover  a 
considerable  extra  circulation.  Just  now,  national  banks  whose  deposited  bonds 
are  4 per  cents  could  issue  30  per  cent,  more  circulation  without  exceeding  the 
market  value  of  their  bonds  plus  their  redemption-deposit  of  cash. 


State  Bank  Notes. 


09 


extra  notes  also;  whether  all  banks  in  the  system  should 
have  the  extra-note  privilege,  or  banks  in  certain  cities 
only;  what  features  of  the  law  should  be  left  subject  to 
variation  by  the  Comptroller  of  the  Currency  or  some  other 
executive  officer.  There  ought  to  be  an  arbitrary  maxi- 
mum of  increase,  lest  in  an  occasional  time  of  speculative 
temptation  the  note-issue  should  run  wild;  for  serious 
harm  might  be  done  by  a rapid  increase  long  before  it 
reached  any  automatic  check  by  redemption.  Both  of  the 
plans  need  free  criticism  and  working  out  in  detail  by  prac- 
tical bankers  before  either  can  be  trusted;  but  the  point  I 
wish  to  urge  is,  that  some  such  special  provision  must  be 
made  to  insure  a return  of  the  note-circulation  to  its 
former  volume,  or  it  will  probably  increase. 

In  any  bank  note  system,  the  whole  volume  of  notes 
below  the  lowest  point  reached  in  the  duller  times  is  dead 
and  useless  for  purposes  of  elasticity.  It  is  only  the  flow 
and  ebb  that  give  the  elasticity;  if  the  notes  never  fall  be- 
low 100  millions,  that  100  millions  might  as  well  be  coin.* 
We  may  accordingly,  if  we  please,  rid  ourselves  of  practi- 
cally all  the  present  ordinary  note-circulation,  substitute 
coin  for  it,  and  still  have  the  desired  elasticity  by  using 
the  extra  notes  of  one  of  the  two  plans  described  above. 
Of  course  the  reduction  ought  to  be  made  gradually,  and 
by  the  weight  of  conditions  that  do  not  affect  the  extra 
notes,  e.  g.,  by  a higher  tax. 

OBJECTIONS  TO  STATE  BANK  NOTES. 

It  is  hard  to  see  why  the  national  bank  system,  as  such, 
should  be  blamed  for  its  failure  to  be  elastic.  Any  state 
bank  system  must  be  subject  to  the  same  natural  laws. 
£he  transfer  of  supervision  to  the  State  governments  makes 
no  change  whatever  in  the  rule  that  the  increase  or  de- 
crease of  note-circulation  will  be  determined  by  the  excess 
of  the  profits  over  the  checks  or  of  the  checks  over  the 
profits;  that  rule  is,  from  the  nature  of  the  case,  unchange- 

* Except  that  the  change  might  introduce  some  additional  difficulty  into  the 
arrangements  for  putting  good  security  behind  the  extra  notes,  and  the  notes 
might  become  unfamiliar  enough  to  be  a little  less  convenient  as  money. 


70 


Colorado  College  Studies. 


able.  All  that  can  be  done  is  to  vary  the  nature  of  the 
checks;  and  wherever  that  can  be  done  by  the  state  gov- 
ernments it  can  be  done  by  the  national  government.  If 
it  is  desired  to  increase  the  note-circulation,  that  end  is 
reached  as  certainly  by  removing  taxes  from  national  bank 
circulation  as  by  removing  them  from  state  bank  circula- 
tion. If  it  is  desired  to  make  temporary  contractions  easier, 
by  reducing  the  expense  and  trouble  of  withdrawing  de- 
posited bonds  and  redeeming  the  notes,  or  to  adopt  the  Knox 
plan  or  the  second  plan  described  in  this  article,  every 
detail  of  the  improved  process  can  be  applied  by  the  na- 
tional government  as  easily  as  by  the  state  governments, 
and  indeed  with  less  expense.  Anything  that  would  be 
dangerous  in  a national  bank  note  system  would  be  as 
dangerous  (and  usually  more  dangerous)  in  a state  bank 
note  system.  And  any  imaginable  gain  under  state  super- 
vision can  be  had  as  well  or  better  under  national  super- 
vision. 

The  difficulty  of  framing  a good  system  of  bank  note 
law  and  supervision  by  forty-four  distinct  legislatures  needs 
no  detailed  discussion,  unless  by  a competent  humorist. 
There  is  no  hope  that  a jumble  of  various  state-systems 
would  “ average  up”  into  a good  bank-note  circulation.  If 
in  ten  states,  five  states,  one  state,  the  system  is  bad, 
there  will  appear  bank  notes  imperfectly  guarded  by  secu- 
rities or  dependent  upon  too  small  a reserve,  in  which  case 
it  is  only  a question  of  time  when  some  bank  will  let  its 
notes  go  to  protest;  to  say  nothing  of  the  moral  certainty 
that  the  wish  of  the  legislatures  to  see  the  new  system  well 
started  would  cause  the  checks  upon  profits  to  be  set  too 
low,  so  that  (taking  the  country  through)  there  would  b<£ 
a large  unnecessary  original  issue  of  notes,  coming  beforfi 
any  need  of  trade  called  for  them,  and  merely  crowding 
out  better  money.*  In  whatever  states  the  notes  were 
insecure,  those  states  would  suffer  annoyance  and  occa- 
sional loss  by  circulation  of  such  notes;  some  of  the  notes 

* This  point  has  not  received  the  attention  it  deserves.  Its  practical  impor- 
tance is  great. 


State  Bank  Notes. 


71 


would  pass  into  other  states  and  carry  annoyance  with 
them;  and  the  repute  of  good  notes  would  be  injured  out- 
side of  the  state  of  their  origin,  because  many  men  would 
not  take  the  trouble  to  remember  which  states  were  sound, 
and  would  look  with  distrust  upon  any  notes  of  a distant 
state,  perhaps  of  any  state  but  their  own.  Unless  all  the 
states  agreed  upon  the  same  paper  and  similar  printing, 
the  detection  of  counterfeits  would  once  more  become  a 
fine  art,  and  the  unskilled  man  and  woman  would  be  daily 
exposed  to  loss.  It  is  not  enough  to  answer  that  there  is 
no  danger  of  the  return  of  the  absurd  and  dangerous  bank 
money  of  the  first  half  of  the  century;  if  there  is  any 
failure  to  redeem  notes,  any  discount  upon  some  notes  of 
distant  origin  or  of  tarnished  fame,  the  opportunity  of 
petty  fraud  upon  the  ignorant  and  careless  is  thrown  wide 
open,  and  every  man  must  choose  between  possible  loss 
and  the  vexatious  precaution  of  examining  every  note  he 
receives.  Moreover,  the  workman  in  taking  wages,  the 
retail  dealer  in  taking  payment  from  a customer  he  is 
anxious  to  retain,  is  often  reluctant  to  give  offense  by  ob- 
jecting to  money  on  the  mere  chance  that  it  is  depreciated, 
and  will  sometimes  take  it  when  he  knows  there  will  be  a 
small  depreciation,  rather  than  raise  the  objection.  The 
presence  in  any  money  system  of  elements  that  are  dis- 
trusted, that  must  be  looked  for  and  chaffered  over  or  sub- 
ject the  recipient  to  loss,  is  so  wearisome  an  addition  to 
the  friction  of  trade  that  a clear  case  of  beneficence  in 
other  directions  (and  no  small  beneficence)  must  be  shown 
to  give  such  kinds  of  money  any  claim  to  consideration. 
And  when  such  beneficence  as  state  bank  notes  are  capa- 
ble of  can  be  had  without  the  friction  and  annoyance  by 
using  national  bank  notes  instead,  the  attempt  to  substi- 
tute the  former  seems  a ludicrous  folly.  Even  if  we  im- 
agine the  prodigy  of  wise  concurrent  action  of  all  the 
states  at  first,  what  guaranty  is  there  against  the  appear- 
ance from  time  to  time  hereafter  of  those  legislatures  whose 
pride  it  is  to  despise  experience,  to  brush  aside  the  sophis- 
tries of  prejudiced  conservatives,  and  to  open  short  cuts  to 


72 


Colorado  College  Studies. 


prosperity  for  the  oppressed  plain  people?  Many  of  the 
advocates  of  restoration  of  state  bank  notes  see  the  diffi- 
culties distinctly  enough  to  propose  that  there  shall  still 
be  some  national  restriction  and  supervision.  The  best 
that  can  be  said  of  such  plans  is  that  a safe  built  partly  of 
iron  and  partly  of  wood  will  resist  fire  better  than  a safe 
built  wholly  of  wood.  The  advocates  of  an  admixture  of 
wood  may  fairly  be  asked  what  good  is  expected  from  the 
change. 

If  we  are  to  attempt  elasticity,  then,  common  prudence 
requires  the  preference  of  national  bank  notes  to  state  bank 
notes;  for  any  tolerable  system  of  so-called  state  bank 
notes  must  include  national  control  so  nearly  complete 
that  it  is  really  a national  bank  note  system. 


III.— INCREASE  OF  SCANTY  LOCAL  CIRCULATION. 

So  far  as  it  deals  with  the  increased  demand  at  crop- 
moving  time,  this  argument  for  state  bank  notes  is  of  course 
mere  repetition  of  the  argument  from  elasticity;  but  a 
separate  place  may  be  given  to  it  because  some  persons 
have  seriously  urged  that  the  permanent  stock  of  money 
could  thus  be  increased  in  the  regions  where  a scarcity  is 
now  felt.  Taken  in  this  sense,  even,  it  is  completely  an- 
swered by  the  answer  to  the  elasticity  argument;  for  if 
there  is  any  way  by  which  state  bank  notes  could  give  a 
larger  permanent  money  circulation  to  parts  of  the  country, 
the  same  way  can  be  provided  for  national  bank  notes  by 
national  law  and  supervision.  And  if  this  were  not  so, 
the  proposed  advantage  of  a larger  local  circulation  is  im- 
aginary. Money  is  sent  away  from  districts  where  capital 
is  scanty  because  goods  are  so  valuable  to  the  farmer,  the 
trader  and  the  manufacturer,  that  they  prefer  having  more 
goods  to  keeping  a comfortable  cash  reserve  in  hand  or  in 
bank;  indeed  they  usually  borrow  besides.  Double  the 
money  in  such  a district,  and  within  two  months  there 
would  be  little  more  than  at  first,  if  it  were  money  that 
could  be  used  in  outside  payments;  in  the  long  run  there 


State  Bank  Notes. 


73 


would  scarcely  be  more,  unless  it  depreciated,  than  if  the 
addition  had  never  been  made.  A district  within  a coun- 
try can  no  more  enlarge  its  permanent  circulation  by  issu- 
ing paper  than  the  country  itself  can;  whatever  nominal 
enlargement  may  appear  will  be  caused  by  depreciation. 
Even  a nominal  permanent  enlargement  could  be  had  only 
through  notes  that  were  objectionable  outside  and  were 
issued  in  such  volume  as  to  exceed*  the  formerly  normal 
amount  of  money  in  the  district;  until  they  reached  that 
volume  they  would  merely  displace  other  money.  With  a 
circulation  thus  enlarged,  the  district  would  enjoy  all  the 
blessings  of  a depreciated  paper  currency  and  a varying 
rate  of  exchange  with  the  outside  world;  and  unless  the 
district  had  a well  defined  frontier  line,  which  is  improb- 
able, there  would  be  a strip  of  country  all  around  it  where 
the  notes  would  be  the  cause  of  daily  disputes  and  frauds. 
If  we  want  this  state  of  things,  we  can  have  it;  but  we  can 
give  the  local  banks  free  rein  just  as  easily  by  national  law 
as  by  state  law. 


IV.— EVILS  OF  THE  TEH  PEE  CENT.  TAX. 

The  objection  to  the  tax  on  state  bank  circulation  ap- 
pears in  two  forms.  One  of  these,  urging  that  individual 
liberty  is  unfairly  dealt  with  by  a prohibitory  tax  on  bank 
notes  that  fail  to  conform  to  legally  set  rules,  must  be  the 
product  of  hasty  writing  without  second  thought.  Surely 
the  creation  of  money  is,  like  marriage,  “affected  by  a 
public  interest,”  and  subject  to  the  right  of  the  whole 
community  to  protect  its  interest  by  prescribing  conditions 
for  every  such  transaction.  Does  any  one  (except  those 
who  follow  their  truth  wherever  it  leads,  with  a Tolstoi- 
like  disregard  of  consequences  and  of  other  truths)  pro- 
pose that  every  mushroom  bank  or  factory  store  shall 
be  left  free  to  circulate  its  notes  or  “orders”  as  money 
where  it  can?  If  not,  some  power  must  prohibit,  and  prac- 

* Strictly,  of  course,  allowance  must  be  made  for  the  scattered  remains  of 
the  former  money,  and  conversely  for  the  increasing  needs  of  trade.  And  to  cause 
the  inflation  the  notes  must  become  practically  inconvertible. 


74 


Colorado  College  Studies. 


tically  the  power  must  be  either  the  Nation  or  the  State. 
Here  rises  the  other  form  of  the  argument:  that  the  pro- 
hibitory tax  goes  beyond  the  constitutional  powers  of  Con- 
gress. Such  a claim  can  be  maintained  only  as  a protest 
against  the  decision  of  the  Supreme  Court,  like  the  still 
existing  dissent  from  the  Legal  Tender  decision.  There 
is  no  room  for  the  claim  of  “moral”  unconstitutionality, 
such  as  there  might  have  been  if  the  Court  had  merely 
sustained  the  law  in  its  formal  aspect  of  laying  a tax,  for 
the  decision  was  not  reached  by  ignoring  the  prohibitory 
nature  of  the  tax,  but  by  affirming  the  power  to  prohibit. 
The  words  are:  “Congress  may  restrain  by  suitable  enact- 
ments the  circulation  as  money  of  any  notes  not  issued 
under  its  own  authority.”  Ought  Congress  to  retreat  be- 
fore constitutional  scruples  which  have  (to  state  the  case 
mildly)  nothing  near  unanimity  of  legal  opinion  to  sup- 
port them  and  have  already  been  overruled  by  the  Supreme 
Court,  scruples  'which  at  best  affect  merely  the  question 
whether  Congress  or  the  State  legislatures  shall  use  a power 
that  one  or  the  other  must  use;  when  the  abandonment  of 
the  field  by  Congress  would  expose  the  country  to  the  in- 
evitable evils  of  disjointed  management  of  note-circulation 
by  the  separate  States?  If  any  one  holds  that  decision  of 
the  Supreme  Court  to  be  erroneous,  he, might  better  aim 
to  cure  the  error  by  a constitutional  amendment  than  to 
put  upon  the  country  the  needless  and  ridiculous  embar- 
rassments that  state  bank  paper  would  inflict. 


Between  national  bank  notes  and  state  bank  notes,  then, 
the  choice  seems  too  easy  to  be  called  a problem.  The  real 
bank-note  question  is  whether  we  need  any  bank  notes  at 
all;  and  if  we  do,  how,  under  national  control,  they  can  be 
kept  secure  and  their  volume  can  be  made  elastic.  The 
latter  part  of  the  subject  has  had  a fairly  full  public  dis- 
cussion, but  too  little  attention  has  been  given  to  the  pos- 
sibility of  doing  without  bank  notes.  That  the  withdrawal 
of  the  present  stock  of  bank  notes  would  not  probably  be 


State  Bank  Notes. 


75 


a troublesome  process,  has  been  shown  in  the  earlier  part 
of  this  paper.  And  if  it  is  thought  necessary  to  secure  for 
the  money-supply  an  elasticity  of  volume,  in  addition  to 
the  existing  virtual  elasticity  by  change  of  speed  in  circu- 
lation and  by  additions  of  metal,  it  is  possible  to  have 

elasticity  without  notes. 

Our  choice  of  means  is  not  restricted  to  notes.  The 
Treasury  itself  is  a ready-made  apparatus.  Whenever 
Treasury  receipts  exceed  Treasury  payments,  the  circula- 
tion outside  contracts;*  wdienever  the  payments  predomi- 
nate, the  circulation  enlarges.  When  such  a change  comes 
without  any  corresponding  need  of  trade,  the  disparity  is 
set  right  by  the  usual  automatic  methods,  i.  e.  by  a quick- 
ening of  the  average  speed  of  circulation  or  an  increase  of 
bank  reserves  in  the  cases  of  needless  contraction  and  ex- 
pansion respectively,  followed  (if  the  disparity  is  large 
enough  and  lasts  long  enough)  by  a change  in  the  rate  of 
short-time  interest  and  ultimately  by  a change  in  the  ex- 
port or  import  of  metal.  When  the  expansion  or  contrac- 
tion happens  to  fit  a need  of  trade,  we  have  a true  elasticity 
imparted  by  the  Treasury  action.  In  fact,  several  impor- 
tant outpours  and.  absorptions  of  money  by  the  Treasury 
occur  every  year;  if  they  could  be  made  to  fit  the  needs  of 
trade  better  than  they  do  now,  the  circulation  would  be 
made  elastic  pro  tanto.  For  instance,  nearly  all  the  in- 
terest on  the  public  debt  is  paid  in  April  and  the  corre- 
sponding quarter  months,  now  that  the  interest-bearing 
debt  is  mostly  the  1907  four  per  cents.  If  the  interest  were 
made  semi-annual,  and  payable  in  March  and  September, 
about  11  millions  f of  interest-money  would  be  cast  into  the 
channels  of  business  at  crop-moving  time,  and  another  11 
millions  in  time  for  the  spring  trade,  while  there  would 
be  a corresponding  contracting  influence  at  work  through 

* Contracts  relatively  ; that  is,  if  greater  forces  are  just  then  expanding  it, 
Treasury  action  merely  diminishes  the  expansion.  The  word  “ enlarges,”  in  the 
next  phrase,  is  used  in  the  same  relative  sense,  though  the  enlargement  is  usually 
absolute  also. 

t Instead  of  the  present  arrangement  of  514  millions  in  October,  and  514  more 
in  January,  when  it  is  not  wanted. 


76 


Colorado  College  Studies. 


the  summer  and  the  winter,  when  it  is  wanted.  Again,  the 
pensions  are  paid  quarterly,  but  are  distributed  in  groups 
upon  different  sets  of  quarter-days.  These  might  be  so 
grouped,  probably  without  serious  inconvenience  to  the 
pensioners,*  that  the  payments  in  two  months  of  spring 
should  be  about  twice  as  large  and  in  two  months  of  autumn 
about  three  times  as  large  as  at  other  times.  With  pen- 
sions amounting  to  160  or  180  millions  annually,  such  an 
arrangement  could  be  made  to  “plump”  an  extra  30  or  40 
millions  in  the  autumn  and  half  of  that  in  the  spring. 
Without  recommending  these  particular  methods,  one  may 
take  them  as  illustrating  the  possibility  of  such  adjust- 
ments. Other  means,  some  of  which  are  applied  by  the 
Treasury,  are  the  purchase  of  bonds  at  the  end  of  summer, 
the  increase  of  Treasury  deposits  with  the  banks,  the  ar- 
rangement of  contracts  so  as  to  make  the  principal  pay- 
ments for  supplies  in  the  autumn  and  spring. 

It  is  a fair  question  for  debate  whether  this  paternal- 
looking  behavior  of  the  Treasury  would  be  good  policy  in 
the  long  run.  The  objection  to  it  as  government  inter- 
ference is  sound.  But  as  compared  with  the  present  Treas- 
ury methods,  it  would  be  only  a better  arrangement  of  ebbs 
and  flows  that  exist  already  in  considerable  degree  and 
often  at  the  wrong  times.f  Whatever  evils  it  has,  the 
Treasury  method  of  obtaining  elasticity  is  perhaps  better 
than  any  known  bank-note  system,  and  is  far  better  than 
any  possible  state  bank  system.  In  the  long  run,  among 
fallible  men,  expensive  money  is  the  most  economical; 
money  that  cannot  be  duplicated  without  a liberal  expense 
of  labor;  metal,  or  certificates  known  to  have  their  full 
equivalent  of  metal  behind  them.  In  the  sacrifice  a coun- 
try necessarily  makes  to  obtain  such  money,  as  compared 

*Crudel/,  by  making  a part  of  the  pensions  semi-annual,  with  the  autumnal 
payment  larger  than  the  other ; an  inequality  that  fits  tolerably  well  the  needs  of 
indigent  pensioners. 

fSee  illustrative  figures  in  Mr.  Kinley’s  article  on  the  Independent  Treasury 
in  the  Annals  of  the  American  Academy  of  Political  and  Social  Science , Septem- 
ber, 1892.  The  figures  are  for  operations  at  New  York,  but  are  a sufficient  indica- 
tion of  what  happens  in  the  whole  country. 


State  Bank  Notes. 


77 


with  watering  it  by  a note-element,  it  is  buying  business 
security  and  a charm  against  popular  delusions.  Some- 
thing might  be  said,  even  if  no  project  for  elasticity 
through  Treasury  payments  is  accepted,  for  the  belief 
that  our  best  policy  is  to  prefer  safety  to  elasticity,  to 
arrange  the  checks  on  profit  so  as  to  insure  the  gradual 
extinction  of  the  bank  notes,*  to  substitute  nothing  for 
them,  and  so  let  coin  flow  in;  when  that  is  done,  to  increase 
the  coin  reserve  against  greenbacks  by  15  or  20  millions 
annually  till  it  equals  the  whole  volume  of  greenbacks  and 
they  can  be  converted  into  coin  certificates.  When  a gen- 
eration has  grown  up  that  has  never  seen  a bank  note  or  a 
government  note,  the  seed  of  many  a folly  will  be  dead  in 
the  popular  mind. 


The  principal  conclusions  we  have  reached  may  be 
summarized  as  follows: 

1.  The  extinction  of  the  national  bank  notes  requires 
no  creation  of  other  money.  The  coin  to  take  their  place 
will  come  in  without  perceptibly  greater  national  sacrifice 
than  has  attended  the  extinction  of  a still  larger  amount  of 
notes  in  the  past  few  years. 

2.  An  elastic  bank  note  system  would  probably  cause 
progressive  increase  in  the  amount  of  note-circulation, 
unless  restraints  hitherto  unusual  were  applied.  Such  re- 
straint might  be  given  by  causing  the  notes  added  in  the 
temporary  expansions  to  bear  interest  after  a set  time,  or 
by  expressly  requiring  the  issuing  banks  to  reduce  their 
circulation  within  the  old  limits  before  a set  time. 

3.  Nothing  is  to  be  gained,  either  towards  elasticity  or 
towards  permanent  enlargement  of  local  circulation,  by 
substitution  of  state  control  for  national  control.  The  in- 
crease or  diminution  of  bank  notes  is  determined  by  the 
relation  between  the  profits  and  certain  well  defined  checks, 
and  the  state  governments  cannot  apply  the  checks  better 
than  the  national  government  can. 


* Which  of  course  does  not  imply  a disappearance  of  the  national  bank  system. 


78 


Colorado  College  Studies. 


4.  The  relegation  of  control  to  the  states  would  almost 
certainly  cause  the  checks  to  be  set  too  low  at  first,  and 
cause  a large  initial  increase  of  notes. 

5.  Insecure  notes  from  a single  state  would  diminish 
the  practical  convenience  of  the  whole  note-circulation. 

6.  Security  of  all  the  notes  under  separate  state  man- 
agement is  almost  incredibly  improbable;  and  if  attained 
in  one  year,  might  easily  fail  in  the  next. 

7.  The  prohibition,  by  tax  or  otherwise,  of  circulating 
notes  that  fail  to  conform  with  national  law,  is  not  an  in- 
justice to  individuals.  The  objection  on  constitutional 
grounds  touches  only  the  question  whether  state  or  na- 
tional legislatures  shall  impose  the  necessary  restrictions; 
and  if  sound  at  all,  is  rather  an  argument  for  a constitu- 
tional amendment  than  for  a bad  money  system. 

8.  A means  of  elasticity,  probably  safer  than  any  bank 
note  system,  exists  in  the  irregularity  of  Treasury  expenses. 


(^OLORADO  (^OLLEGE, 

Goforado  Springs,  Golo* 


y*T^HE  College  offers  two  courses,  leading,  respectively,  to 
^ the  degrees  of  Bachelor  of  Arts  and  Bachelor  of 
Philosophy.  In  the  Pli.  B.  Course,  Greek  is  omitted  and 
more  attention  is  given  to  the  sciences  and  modern  lan- 
guages. The  College  has  a good  library  and  well-equipped 
laboratories. 


The  various  courses  of  study  have  been  so  arranged 
and  the  faculty  so  enlarged  that  Colorado  College  offers 
the  same  educational  facilities  as  the  Eastern  colleges. 

For  catalogues,  address 


Wm. 


F.  Slocum, 

President. 


The  Cutler  Academy, 

Under  the  auspices  of  the  Colorado  College,  gives  students 
a thorough  preparation  for  admission  to  the  Freshman 
class  of  any  college  in  the  country.  Correspondence  con- 
cerning the  Cutler  Academy  should  be  addressed  to  the 
Assistant  Principal,  ~ n 


The  Location  of  the  College  is  unsurpassed.  Colorado  Springs 
has  a world-wide  reputation  as  a Health  Resort. 


Students  forced  by  pulmonary  or  malarial  troubles  to 
discontinue  their  studies  in  the  East,  pursue  college  courses 
here  successfully  an(}  at  the  same  time  make  a permanent 
gain  in  health. 


THE  COBURN  LIBRARY, 


- 


'■4 


